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Chapters
1: Goods and Services Tax (G.S.T.)
2: Banking
3: Shares and Dividends
UNIT 2: ALGEBRA
4: Linear Inequations
▶ 5: Quadratic Equation
6: Problems on Quadratic Equations
7: Ratio and Proportion
Chapter 8: Remainder Theorem and Factor Theorem
9: Matrices
Chapter 10: Arithmetic Progression
Chapter 11: Geometric Progression
12: Reflection
Chapter 13: Section and Mid-point Formulae
Chapter 14: Equation of a Straight Line
UNIT 3: GEOMETRY
Chapter 15: Similarity (As a Size Transformation)
Chapter 16: Similarity of Triangles
17: Loci
Chapter 18: Angle and Cyclic Properties of a Circle
Chapter 19: Tangent Properties of Circles
20: Constructions
UNIT 4: MENSURATION
Chapter 21: Volume and Surface Area of Solids (Cylinder, Cone and Sphere)
UNIT 5: TRIGONOMETRY
Chapter 22: Trigonometrical Identities
Chapter 23: Heights and Distances
UNIT 6: STATISTICS
Chapter 24: Graphical Representation of Statistical Data
Chapter 25: Measures of Central Tendency (Mean)
Chapter 26: Median, Quartiles and Mode
UNIT 7: PROBABILITY
Chapter 27: Probability
![R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 5 - Quadratic Equation - Shaalaa.com](/images/mathematics-english-class-10-icse_6:af235bdb1c1648d185f85c25aa96a7cd.jpg "R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 5 - Quadratic Equation")
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Solutions for Chapter 5: Quadratic Equation
Below listed, you can find solutions for Chapter 5 of CISCE R.S. Aggarwal for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई.
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई 5 Quadratic Equation EXERCISE 5A [Pages 56 - 57]
Find which of the following are the solutions of the equation 6x2 – x – 2 = 0?
(i) `1/2`
(ii) `(-1)/2`
(iii) `2/3`
Determine whether `x = (-1)/3` and `x = 2/3` are the solutions of the equation 9x2 – 3x – 2 = 0.
Solve the following equation by factorization:
16x2 = 25
Solve the following equation by factorization:
x2 + 2x = 24
Solve the following equation by factorization:
x2 – x = 156
Solve the following equation by factorization:
x2 – 11x = 42
Solve the following equation by factorization:
x2 – 7x + 10 = 0
Solve the following equation by factorization:
x2 + 18x = 40
Solve the following equation by factorization:
x2 + 17 = 18x
Solve the following equation by factorization:
3x2 = 5x
Solve the following equation by factorization:
(x + 3)(x – 3) = 27
Solve the following equation by factorization:
x2 – 30x + 216 = 0
Solve the following equation by factorization:
12x2 + 29x + 14 = 0
Solve the following equation by factorization:
2x2 – 7x = 39
Solve the following equation by factorization:
10x2 = 9x + 7
Solve the following equation by factorization:
15x2 – 28 = x
Solve the following equation by factorization:
8x2 + 15 = 26x
Solve the following equation by factorization:
3x2 + 8 = 10x
Solve the following equation by factorization:
x(6x – 11) = 35
Solve the following equation by factorization:
6x(3x – 7) = 7(7 – 3x)
Solve the following equation by factorization:
2x2 – 9x + 10 = 0, when (i) x ∈ N (ii) x ∈ Q
Solve the following equation by factorization:
4x2 – 9x – 100 = 0, when x ∈ Q
Solve the following equation by factorization:
3x2 + 11x + 10 = 0, when x ∈ I
Solve the following equation by factorization:
`x + 1/x = 3 1/3, x ≠ 0`
Solve the following equation by factorization:
`5x - 35/x = 18`
Solve the following equation by factorization:
`10x - 1/x = 3`
Solve the following equation by factorization:
Зa2x2 + 8abx + 4b2 = 0, a ≠ 0
Solve the following equation by factorization:
4x2 – 4ax + (a2 – b2) = 0, where a, b ∈ R
[Hint: Given equation may be written as: 4x2 – 2(a + b)x – 2(a – b)x + (a2 – b2) = 0]
Solve the following equation by factorization:
5x2 – 12x – 9 = 0, when (i) x ∈ I (ii) x ∈ Q
Solve the following equation by factorization:
2x2 – 11x + 15 = 0, when (i) x ∈ N (ii) x ∈ I
Solve the following equation by factorization:
`sqrt(3)x^2 + 11x + 6sqrt(3) = 0`
Solve the following equation by factorization:
`2sqrt(5)x^2 - 3x - sqrt(5) = 0`
Solve the following equation by factorization:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
Solve the following equation by factorization:
`(x + 1)/(x - 1) = (3x - 7)/(2x - 5)`
Solve the following equation by factorization:
`(3x + 1)/(7x + 1) = (5x + 1)/(7x + 5)`
Solve the following equation by factorization:
`5/((2x + 1)) + 6/((x + 1)) = 3`
Solve the following equation by factorization:
`(2x)/(x - 4) + (2x - 5)/(x - 3) = 25/3`
Solve the following equation by factorization:
`(x + 3)/(x - 2) - (1 - x)/x = 4 1/4`
Solve the following equation by factorization:
`1/((x - 2)) + 2/((x - 1)) = 6/x`
Solve the following equation by factorization:
`2(x/(x + 1))^2 - 5(x/(x + 1)) + 2 = 0, x ≠ -1`
Solve the following equation by factorization:
5(3x + 1)2 + 6(3x + 1) – 8 = 0
Solve the following equation by factorization:
`sqrt(x + 15) + (x + 3)`
Solve the following equation by factorization:
`sqrt(2x + 9) = (13 - x)`
Solve the following equation by factorization:
`sqrt(3x^2 - 2) = (2x - 1)`
Solve the following equation by factorization:
`sqrt(3x^2 + x + 5) = (x - 3)`
Find the quadratic equation whose solution set is {2, –3}.
Find the quadratic equation whose solution set is `{-3, 2/5}`.
Find the quadratic equation whose solution set is `{2/5, -1/2}`.
Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x2 – kx + 6 = 0. Thus, find the other root of the equation.
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई 5 Quadratic Equation EXERCISE 5B [Pages 61 - 62]
Solve the following equation using quadratic formula:
x2 – 4x + 1 = 0
Solve the following equation using quadratic formula:
9x2 + 7x – 2 = 0
Solve the following equation using quadratic formula:
`3/4 x^2 - x - 1 = 0`
Solve the following equation using quadratic formula:
4 – 11x = 3x2
Solve the following equation using quadratic formula:
25x2 + 30x + 7 = 0
Solve the following equation using quadratic formula:
5x2 – 19x + 17 = 0
Solve the following equation using quadratic formula:
3x2 – 8x + 2 = 0
Solve the following equation using quadratic formula:
`sqrt(3)x^2 + 10x - 8sqrt(3) = 0`
Solve the following equation using quadratic formula:
`2x^2 + sqrt(7)x - 7 = 0`
Solve the following equation using quadratic formula:
6x2 – 31x = 105
Solve the following equation using quadratic formula:
`(x + 3)/(2x + 3) = (x + 1)/(3x + 2)`
Solve the following equation using quadratic formula:
`(x - 1)/(x - 2) + (x - 3)/(x - 4) = 3 1/3`
Solve for x and give your answer correct to 2 decimal places:
x2 – 10x + 6 = 0
Solve for x and give your answer correct to 2 decimal places:
2x2 – 6x + 3 = 0
Solve for x and give your answer correct to 2 decimal places:
3x2 – 32x + 12 = 0
Solve for x and give your answer correct to 2 decimal places:
x2 + 7x = 7
Solve for x and give your answer correct to 2 decimal places:
3x2 – x – 7 = 0
Solve for x and give your answer correct to 2 decimal places:
4x2 – 7x + 2 = 0
Solve for x and give your answer correct to 2 decimal places:
x2 – 7x + 3 = 0
Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:
x2 – 5x – 10 = 0
Solve for x the quadratic equation x2 – 4x – 8 = 0. Give your answer correct to three significant figures.
Solve the following quadratic equation: x2 + 4x – 8 = 0. Give your answer correct to one decimal place.
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई 5 Quadratic Equation EXERCISE 5C [Page 65]
Discuss the nature of the roots of the following equation without actually solving it:
x2 – 8x + 7 = 0
Discuss the nature of the roots of the following equation without actually solving it:
6x2 + 7x – 10 = 0
Discuss the nature of the roots of the following equation without actually solving it:
25x2 + 30x + 7 = 0
Discuss the nature of the roots of the following equation without actually solving it:
15x2 – 28 = x
Discuss the nature of the roots of the following equation without actually solving it:
16x2 = 24x + 1
Discuss the nature of the roots of the following equation without actually solving it:
`2x^2 - 2sqrt(6)x + 3 = 0`
Discuss the nature of the roots of the following equations without actually solving it:
2x2 + 2x + 3 = 0
Discuss the nature of the roots of the following equation without actually solving it:
2x2 – 5x – 4 = 0
Discuss the nature of the roots of the following equation without actually solving it:
5x2 – 13x – 6 = 0
Discuss the nature of the roots of the following equation without actually solving it:
9x2 – 6x + 1 = 0
Discuss the nature of the roots of the following equation without actually solving it:
3x2 – 2x + 5 = 0
Discuss the nature of the roots of the following equation without actually solving it:
`x^2 + 2sqrt(3)x - 1 = 0`
Find the values of k for which the following equation has equal roots:
9x2 + kx + 1 = 0
Find the values of k for which the following equation has equal roots:
x2 – 2kx + 7k – 12 = 0
Find the values of k for which the following equation has equal roots:
(3k + 1)x2 + 2(k + 1)x + k = 0
Find the values of k for which the following equation has equal roots:
x2 – 2(5 + 2k)x + 3(7 + 10k) = 0
Find the values of k for which the following equation has equal roots:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
Find the values of k for which the following equation has equal roots:
kx2 + kx + 1 = –4x2 – x
Find the values of k for which the following equation has equal roots:
3kx2 = 4(kx – 1)
Find the values of k for which the following equation has equal roots:
x2 + 4kx + (k2 – k + 2) = 0
Show that the equation x2 + ax – 1 = 0 has real and distinct roots for all real values of x.
[Hint: D = (a2 + 4) > 0.]
Show that the equation 3x2 + 7x + 8 = 0 is not true for any real value of x.
[Hint: D = (49 – 4 × 3 × 8) = (49 – 96) = – 47 < 0.]
If the roots of the equation (c2 – ab)x2 – 2(a2 – bc)x + (b2 – ac) = 0 are real and equal, show that either a = 0 or a3 + b3 + c3 = 3abc.
[Hint: D = 4a(a3 + b3 + c3 – 3abc). So, D = 0 ⇒ a = 0 or a3 + b3 + c3 = 3abc.]
If a, b, c ∈ R, show that the roots of the equation (a – b)x2 + (b + c – a)x – с = 0 are rational.
[Hint: D = (a + c – b)2 ≥ 0]
If a, b, c are rational, prove that the roots of the equation (b – c)x2 + (c – a)x + (a – b) = 0 are also rational.
[Hint: D = [(c – a)2 – 4(b – c)(a – b)] = (a + c – 2b)2 ≥ 0.]
CASE STUDY BASED QUESTIONS
| Shridharacharya was an Indian mathematician, Sanskrit Pandit and philosopher from Bengal. He is known for his treatises – Trisatika and Patiganita. He was the first to give an algorithm for solving quadratic equations. His other major works were on algebra, particularly fractions and he gave an exposition on zero. He separated Algebra from Arithmetic. The quadratic formula which is used to find the roots of a quadratic equation is known as Shridharacharya’s rule. |
1. A quadratic equation of the form ax2 + bx + c = 0, a ≠ 0, has two roots given by:
(a) `x = (b ± sqrt(b^2 - 4abc))/(2a)`
(b) `x = (-b ± sqrt(b^2 - 2ac))/(4a)`
(c) `x = (-b ± sqrt(b^2 - 4ac))/(2ac)`
(d) `x = (-b ± sqrt(b^2 - 4ac))/(2a)`
2. A quadratic equation of the form ax² + bx + c = 0, a ≠ 0, has rational roots, if the value of (b2 – 4ac) is:
(a) less than 0
(b) greater than 0
(c) equal to 0
(d) equal to 0 or a perfect square
3. The maximum number of roots that a quadratic equation can have is:
(a) 1
(b) 2
(c) 3
(d) 4
4. A quadratic equation ax2 + bx + c = 0, a ≠ 0, having real coefficients, cannot have real roots if:
(a) b2 – 4ac < 0
(b) b2 – 4ac = 0
(c) b2 – 4ac > 0
(d) b2 – 4ac ≥ 0
5. The quadratic equation, x2 + 26x + 169 = 0, has:
(a) non real roots
(b) rational and unequal roots
(c) equal roots
(d) irrational roots
|
Raman Lal runs a stationery shop in Pune. The analysis of his sales, expenditures and profits showed that for x number of notebooks sold, the weekly profit (in ₹) was P(x) = –2x2 + 88x – 680. Raman Lal found that:
|
Now answer the following questions:
1. What will be Raman Lal’s profit if he sold 20 notebooks in a week?
- ₹ 144
- ₹ 280
- ₹ 340
- ₹ 560
2. What is the maximum profit that Raman Lal can earn in a week?
- ₹ 144
- ₹ 288
- ₹ 340
- ₹ 680
3. What is Raman Lal’s loss if he does not sell any notebooks in a particular week?
- ₹ 0
- ₹ 340
- ₹ 680
- ₹ 960
4. Write a quadratic equation for the condition when Raman Lal does not have any profit or loss during a week.
- 2x2 – 44x + 340 = 0
- x2 + 44x – 340 = 0
- x2 – 88x + 340 = 0
- x2 – 44x + 340 = 0
5. What is the minimum number of notebooks x that Raman Lal should sell in a week so that he does not incur any loss?
- 0
- 10
- 11
- 12
ASSERTION-REASON QUESTIONS Directions: In each of the following, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:
Assertion (A): The discriminant of the quadratic equation `x^2 + 2sqrt(2)x + 1 = 0` is less than zero.
Reason (R): The discriminant of the quadratic equation ax2 + bx + c = 0 is `sqrt(b^2 - 4ac)`.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): The quadratic equation 3kx2 – 4kx + 4 = 0 has equal roots, if k = 3.
Reason (R): For equal roots of a quadratic equation, we must have D = 0.
A is true, R is the false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): The roots of the quadratic equation 3x2 + 7x + 8 = 0 are imaginary.
Reason (R): The discriminant of a quadratic equation is always positive.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): The roots of the quadratic equation 8x2 + 2x – 3 = 0 are `-1/2` and `3/4`.
Reason (R): The roots of the quadratic equation ax2 + bx + c = 0 are given by `x = (-b ± sqrt(b^2 - 4ac))/(2a)`
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई 5 Quadratic Equation COMPETENCY-FOCUSED QUESTIONS [Pages 66 - 69]
I. Multiple Choice Questions Choose the correct alternative :
The roots of the equation px2 + qx + r = 0, where p ≠ 0, are given by:
`x = (-p ± sqrt(q^2 - 4pr))/(2p)`
`x = (-q ± sqrt(q^2 - 2pr))/(4p)`
`x = (-q ± sqrt(q^2 - 4pr))/(2p)`
`x = (-q ± sqrt(q^2 - 4pr))/(2q)`
The discriminant of the quadratic equation ax2 + bx + c = 0, a ≠ 0 is given by:
b2 – 2ac
b2 – ac
b2 – 4ac
none of these
For real roots of a quadratic equation, the discriminant must be:
greater than or equal to zero
greater than zero
less than or equal to zero
less than zero
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
p2 = 4qr
q2 = 4pr
–q2 = 4pr
p2 > 4pr
If the roots of the quadratic equation, ax2 + bx + c = 0, a ≠ 0 are real and equal, then each root is equal to:
`(-a)/(2b)`
`(-b)/(2a)`
`(-2a)/(b)`
`(-c)/(2a)`
If the discriminant of the quadratic equation, ax2 + bx + c = 0, a ≠ 0 is greater than zero and a perfect square and a, b, c are rational, then the roots are:
rational and equal
irrational and unequal
irrational and equal
rational and unequal
If the discriminant of a quadratic equation, ax2 + bx + c = 0, is greater than zero and a perfect square and b is irrational, then the roots are:
irrational and unequal
irrational and equal
rational and unequal
rational and equal
Which of the following is a quadratic equation?
`x^2 - 2sqrt(x) + 7 = 0`
2x2 – 5x = (x – 1)2
`x - 1/x = 2x^2`
`x^2 + 1/x^2 = 2`
Which of the following is a quadratic equation?
x2 + 1 = (2 – x)2 + 3
2x2 + 3 = (5 + x) (2x – 3)
x3 – x2 = (x – 1)3
none of these
Which of the following is not a quadratic equation?
3x – x2 = x2 + 5
(x + 2)2 = 2(x2 – 5)
`(sqrt(2)x + 3)^2 = 2x^2 + 6`
(x – 1)2 = 3x2 + x – 2
The roots of the quadratic equation 2x2 – x – 6 = 0 are:
`-2, 3/2`
`2, (-3)/2`
`-2, (-3)/2`
`2, (3)/2`
Which of the following quadratic equations has 2 and 3 as its roots?
x2 – 5x + 6 = 0
x2 + 5x + 6 = 0
x2 – 5x – 6 = 0
x2 + 5x – 6 = 0
Which of the following is a root of the quadratic equation, 3x2 + 13x + 14 = 0?
`-1/3`
`-3/2`
`-5/3`
`-7/3`
If `x = -1/2` is a solution of the quadratic equation 3x2 + 2kx – 3 = 0, then the value of k is ______.
`-3/4`
`-5/4`
`-9/4`
`-4/5`
If the equation, x2 – ax + 1 = 0 has two distinct and real roots, then:
|a| ≥ 2
|a| ≤ 2
|a| > 2
|a| < 2
The positive value of k for which the equation x2 + kx + 64 = 0 and x2 – 8x + k = 0 will both have real roots, is ______.
4
8
12
16
If 3 is a root of the quadratic equation x2 – px + 3 = 0, then p is equal to ______.
4
3
5
2
The solution set for the quadratic equation `2x^2 - x + 1/8 = 0` is ______.
`{1/4, 1/4}`
`{-1/4, 1/4}`
`{-1/2, 1/4}`
{4, 4}
The value/s of ‘k’ for which the quadratic equation 2x2 – kx + k = 0 has equal roots is (are):
0 only
4, 0
8 only
0, 8
In solving a quadratic equation, one of the values of the variable x is 233.356. The solution rounded to two significant figures is ______.
233.36
233.35
233.3
230
If the roots of the quadratic equation, px(x – 2) + 6 = 0 are equal, then the value of p is ______.
0
4
6
none of these
If the quadratic equation, `px^2 - 2sqrt(5)px + 15 = 0` has two equal roots, then the value of p is ______.
0
3
6
both 0 and 3
If 1 is a root of the quadratic equation, ky2 + ky + 3 = 0, then the value of k is ______.
`-2/3`
`-1/3`
`-1/2`
`-3/2`
If the equation x2 + 5kx + 16 = 0 has no real roots, then:
`k > 8/5`
`k < -8/5`
`-8/5 < k < 8/5`
none of these
The roots of the quadratic equation 3x2 = 6x is ______.
0
2
0 and 2
0 and 6
The solution set for the quadratic equation 2x2 + kx – k2 = 0 is ______.
{k, k}
{–k, k}
`{-k, k/2}`
`{(-k)/2, k}`
The solution set for the equation, 25x (x + 1) = – 4, is ______.
`{1/5, 4/5}`
`{-1/5, 4/5}`
`{-4/5, -1/5}`
`{-4/5, 1/5}`
The discriminant of the equation, `3x^2 - 2x + 1/3 = 0` is ______.
0
1
2
4
The value of the discriminant of the equation, `sqrt(3)x^2 + 10x + 7sqrt(3) = 0` is ______.
4
16
–16
–12
The value of the discriminant of the equation, `x^2 - (sqrt(2) + 1)x + sqrt(2) = 0` is ______.
`3 + 2sqrt(2)`
`1 - 2sqrt(2)`
`3 - 2sqrt(2)`
`2 - sqrt(2)`
The value of the discriminant of the equation 2x2 – 3x + 5 = 0, is ______.
31
`sqrt(-31)`
`sqrt(31)`
–31
If the equation, ax2 + 2x + a = 0 has two real and equal roots, then:
a = 0, 1
a = 1, 1
a = 0, –1
a = –1, 1
The given quadratic equation `3x^2 + sqrt7x + 2 = 0` has ______.
two equal real roots.
two distinct real roots.
more than two real roots.
no real roots.
What is the nature of the roots of the equation, 2x2 – 6x + 3 = 0?
rational and unequal
irrational and unequal
real and equal
imaginary and unequal
The nature of the roots of the equation, `3x^2 - 4sqrt(3)x + 4 = 0` is ______.
real and equal
irrational and unequal
rational and unequal
imaginary and unequal
If –5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, then the value of k is ______.
`7/4`
`5/4`
`3/4`
`1/4`
III. Analytical and Application Based Questions
Solve for x, if `5/x + 4sqrt(3) = (2sqrt(3))/x^2, x = 0`
Determine whether the following quadratic equation has real roots.
5x2 – 9x + 4 = 0
- Give reasons for your answer.
- If the equation has real roots, identify them.
IV. Case Study Based Questions
|
Raman Lal runs a stationery shop in Pune. The analysis of his sales, expenditures and profits showed that for x number of notebooks sold, the weekly profit (in ₹) was P(x) = –2x2 + 88x – 680. Raman Lal found that:
|
Now answer the following questions:
1. What will be Raman Lal’s profit if he sold 20 notebooks in a week?
- ₹ 144
- ₹ 280
- ₹ 340
- ₹ 560
2. What is the maximum profit that Raman Lal can earn in a week?
- ₹ 144
- ₹ 288
- ₹ 340
- ₹ 680
3. What is Raman Lal’s loss if he does not sell any notebooks in a particular week?
- ₹ 0
- ₹ 340
- ₹ 680
- ₹ 960
4. Write a quadratic equation for the condition when Raman Lal does not have any profit or loss during a week.
- 2x2 – 44x + 340 = 0
- x2 + 44x – 340 = 0
- x2 – 88x + 340 = 0
- x2 – 44x + 340 = 0
5. What is the minimum number of notebooks x that Raman Lal should sell in a week so that he does not incur any loss?
- 0
- 10
- 11
- 12
Solutions for 5: Quadratic Equation
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 5 - Quadratic Equation
Shaalaa.com has the CISCE Mathematics मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. R.S. Aggarwal solutions for Mathematics मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई CISCE 5 (Quadratic Equation) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 5 Quadratic Equation are Method of Solving a Quadratic Equation, Nature of Roots of a Quadratic Equation, Concept of Quadratic Equations, Equations Reducible to Quadratic Equations, Factorisation Method, Quadratic Formula (Shreedharacharya's Rule), Method of Solving a Quadratic Equation, Nature of Roots of a Quadratic Equation, Concept of Quadratic Equations, Equations Reducible to Quadratic Equations, Factorisation Method, Quadratic Formula (Shreedharacharya's Rule).
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