#### Chapters

Chapter 2: Banking (Recurring Deposit Account)

Chapter 3: Shares and Dividend

Chapter 4: Linear Inequations (In one variable)

Chapter 5: Quadratic Equations

Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7: Ratio and Proportion (Including Properties and Uses)

Chapter 8: Remainder and Factor Theorems

Chapter 9: Matrices

Chapter 10: Arithmetic Progression

Chapter 11: Geometric Progression

Chapter 12: Reflection

Chapter 13: Section and Mid-Point Formula

Chapter 14: Equation of a Line

Chapter 15: Similarity (With Applications to Maps and Models)

Chapter 16: Loci (Locus and Its Constructions)

Chapter 17: Circles

Chapter 18: Tangents and Intersecting Chords

Chapter 19: Constructions (Circles)

Chapter 20: Cylinder, Cone and Sphere

Chapter 21: Trigonometrical Identities

Chapter 22: Height and Distances

Chapter 23: Graphical Representation

Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25: Probability

## Chapter 5: Quadratic Equations

#### Exercise 5(A) [Page 54]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 5 Quadratic Equations Exercise 5(A) [Page 54]

Find which of the following equation are quadratic:

(3x - 1)^{2} = 5(x + 8)

Find which of the following equation are quadratic:

5x^{2} - 8x = -3(7 - 2x)

Find which of the following equation are quadratic:

(x - 4)(3x + 1) = (3x - 1)(x +2)

Find which of the following equation are quadratic:

x^{2} + 5x - 5 = (x - 3)^{2}

Find which of the following equations are quadratic:

7x^{3} - 2x^{2} + 10 = (2x - 5)^{2}

Find which of the following equation are quadratic:

(x - 1)^{2} + (x + 2)^{2} + 3(x +1) = 0

Is x = 5 a solution of the quadratic equation x^{2} - 2x - 15 = 0?

Is x = -3 a solution of the quadratic equation 2x^{2} - 7x + 9 = 0?

If `sqrt (2/3)` is a solution of equation 3x^{2} + mx + 2 = 0, find the value of m.

`2/3`and 1 are the solutions of equation mx^{2} + nx + 6 = 0. Find the values of m and n.

If 3 and -3 are the solutions of equation ax^{2} + bx - 9 = 0. Find the values of a and b.

#### Exercise 5(B) [Page 56]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 5 Quadratic Equations Exercise 5(B) [Page 56]

Without solving comment upon the nature of roots of each of the following equations:

7x2 – 9x + 2 = 0

Without solving comment upon the nature of roots of each of the following equations:

6x2 – 13x + 4 = 0

Without solving comment upon the nature of roots of each of the following equations:

`25x^2 − 10x + 1 = 0 `

Without solving comment upon the nature of roots of each of the following equations : `"x"^2+2sqrt3"x"-9=0`

Without solving comment upon the nature of roots of each of the following equations:

`"x"^2 – "ax" – "b"^2 = 0`

Without solving comment upon the nature of roots of each of the following equations:

`2"x"^2 + 8"x" + 9 = 0`

Find the value of p, if the following quadratic equation has equal roots: 4x^{2} – (p – 2)x + 1 = 0

Find the value of 'p', if the following quadratic equations have equal roots :

x^{2} + (p - 3)x + p = 0

The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.

Find the value of m, if the following equation has equal roots : (m – 2)x^{2} – (5+m)x +16 =0

Find the value of k for which the equation 3x^{2}- 6x + k = 0 has distinct and real roots.

#### Exercise 5(C) [Pages 59 - 60]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 5 Quadratic Equations Exercise 5(C) [Pages 59 - 60]

Solve equation using factorisation method:

x^{2} - 10x - 24 = 0

Solve equation using factorisation method:

x^{2} - 16 = 0

Solve equation using factorisation method:

`2"x"^2 = 1/2"x" = 0`

Solve equation using factorisation method:

x (x - 5) = 24

Solve equation using factorisation method:

`9/5"x" = 5 + "x"^2`

Solve equation using factorisation method:

`6/"x" = 1 + "x"`

Solve equation using factorisation method:

x = `(3"x" + 1)/(4"x")`

Solve equation using factorisation method:

x + `1/"x"` = 2.5

Solve equation using factorisation method:

(2x - 3)^{2} = 49

Solve equation using factorisation method:

2(x^{2} - 6) = 3(x - 4)

Solve equation using factorisation method:

(x +1)(2x + 8) = (x + 7)(x +3)

Solve equation using factorisation method:

x^{2} - (a + b) x + ab = 0

Solve equation using factorisation method:

(x - 3)^{2} -4(x +3) -5 = 0

Solve equation using factorisation method:

4(2x - 3)^{2} - (2x - 3) - 14 = 0

Solve equation using factorisation method:

`(3"x" -2)/(2"x" -3) = (3"x" - 8)/("x" + 4)`

Solve equation using factorisation method:

2x^{2} - 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

Solve equation using factorisation method:

`("x" - 3)/("x" + 3) + ("x" + 3)/("x" - 3) = 2 1/2`

Solve equation using factorisation method:

`4/("x" + 2) - 1/("x" + 3) = 4/(2"x" + 1)`

Solve equation using factorisation method:

`5/("x" -2) - 3/("x" + 6) = 4/"x"`

Find the quadratic equation, whose solution set is :

{3,5}

Find the quadratic equation, whose solution set is :

(-2,3}

Solve:

`"x"/3 + 3/(6 - "x") = (2(6 +"x"))/15; (x ≠ 6)`

Solve the equation `9x^2 + (3x)/4 + 2 = 0` if possible for real values of x

Find the value of x, if a + 1=0 and x^{2} + ax - 6 =0.

Find the value of x, if a + 7=0; b + 10=0 and 12x^{2} = ax - b.

Use the substitution y= 2x +3 to solve for x, if 4(2x+3)^{2} – (2x+3) – 14 =0.

Without solving the quadratic equation 6x^{2} – x – 2=0, find whether x = 2/3 is a solution of this equation or not.

Determine whether x = -1 is a root of the equation x^{2} - 3x +2=0 or not.

If x = `2/3` is a solution of the quadratic equation 7x^{2}+mx - 3=0;

Find the value of m.

If x = -3 and x = `2/3` are solutions of quadratic equation mx^{2 }+ 7x + n = 0, find the values of m and n.

If quadratic equation x^{2} - (m + 1) x + 6=0 has one root as x =3;

find the value of m and the root of the equation.

Given that 2 is a root of the equation 3x² – p(x + 1) = 0 and that the equation px² – qx + 9 = 0 has equal roots, find the values of p and q.

Solve : `"x"/"a" - ("a" + "b")/"x" = ("b"("a" + "b"))/"ax"`

Solve : `(1200/"x" + 2)`(x - 10) - 1200 = 60

If -1 and 3 are the roots of x^{2}+px+q=0

then find the values of p and q

#### Exercise 5(D) [Page 64]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 5 Quadratic Equations Exercise 5(D) [Page 64]

Solve the following equation using the formula

`x^2 - 6x = 27`

Solve the following equation using the formula

`x^2 + 10x + 21 = 0`

Solve each of the following equations using the formula:

`x^2 + 6x – 10 = 0`

Solve each of the following equations using the formula:

`x^2 + 2x – 6 = 0`

Solve each of the following equations using the formula:

`3x^2 + 2x – 1 = 0`

Solve the following equations using the formula

`2x^2 + 7x + 5 = 0`

Solve each of the following equations using the formula:

`2/3x=-1/6x^2-1/3`

Solve each of the following equations using the formula:

`1/15x^2+5/3=2/3x`

Solve each of the following equations using the formula:

`x^2-6=2sqrt2x`

Solve each of the following equations using the formula:

`4/x-3=5/(2x+3)`

Solve each of the following equations using the formula :

`(2x+3)/(x+3)=(x+4)/(x+2)`

Solve each of the following equations using the formula:

`sqrt6x^2-4x-2sqrt6=0`

Solve each of the following equations using the formula:

`(2x)/(x-4)+(2x-5)/(x-3)=8 1/3`

Solve each of the following equations using the formula:

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`

Solve the following equations for x and give, in each case, your answer correct to one decimal place :

x^{2} – 8x+5=0

Solve the following equations for x and give, in given case, your answer correct to one decimal place :

5x^{2} +10x – 3 =0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

2x^{2} – 10x +5=0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

4x + `6/x` + 13 = 0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

x^{2} – 3x – 9 =0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

`x^2 - 5x - 10 = 0`

Solve the following equations for x and give, in each case, your answer correct to 3 decimal places

3x^{2} – 12x – 1 =0

Solve each of the following equations for x and give, in each case, your answer correct to 3 decimal places :

x^{2} - 16 x +6= 0

Solve the following equations for x and give, in each case, your answer correct to 3 decimal places

2x^{2} + 11x + 4= 0

Solve :

x^{4} - 2x^{2} - 3 = 0

Solve : x^{4} - 10x^{2} +9 =0

Solve : (x^{2} – x)^{2} + 5(x^{2} – x)+ 4=0

Solve :

(x^{2} - 3x)^{2} - 16(x^{2} - 3x) - 36 =0

Solve:

`sqrt("x"/("x" -3)) + sqrt(("x" -3)/"x") = 5/2`

Solve:

`((2"x" -3)/("x" -1)) - 4(("x" - 1)/(2"x" - 3)) = 3`

Solve:

`((3x + 1)/(x + 1)) + ((x + 1)/(3x + 1)) = 5/2`

Solve the equation `2x - 1/x = 7`.Write your answer correct to two decimal places.

Solve the following equation and give your answer correct to 3 significant figures: 5x² – 3x – 4 = 0

Solve for x using the quadratic formula. Write your answer correct to two significant figures.

(x – 1)^{2} – 3x + 4 = 0

Solve the quadratic equation x^{2} - 3(x + 3) = 0; Give your answer correct two significant figures

#### Exercise 5(E) [Pages 66 - 67]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 5 Quadratic Equations Exercise 5(E) [Pages 66 - 67]

Solve `(2x)/(x - 3) + 1/(2x + 3) + (3x + 9)/((x - 3)(2x +3)) = 0; x != 3, x != - 3/2`

Solve: (2x+3)^{2 }= 81

Solve `a^2x^2 - b^2 = 0`

One root of the quadratic equation `x^2 + (3 - 2a)x - 6a = 0` is -3, find its other root.

Solve `x^2 - 11/4 x + 15/8 = 0`

Solve `x + 4/x = -4; x != 0`

Solve: 2x^{4} – 5x² + 3 = 0

Solve: x^{4} – 2x² – 3 = 0.

Solve `9(x^2 + 1/x^2) - 9(x - 1/x) - 52 = 0`

Solve `2(x^2 + 1/x^2) - (x + 1/x) = 11`

Solve : (x² + 5x + 4)(x² + 5x + 6) = 120

Solve of the following equations, giving answer upto two decimal places.

3x^{2} – x – 7 =0

Solve `(x/(x + 2))^2 - 7(x/(x + 2)) + 12 = 0; x != -2`

Solve : x^{2} – 11x – 12 =0; when x ∈ N

Solve x^{2} – 4x – 12 =0; when x ∈ I

Solve 2x^{2} – 9x + 10 =0; when x ∈ Q

Solve : (a + b)²x² – (a + b)x – 6 = 0; a + b ≠ 0

Solve `1/p + 1/q + 1/x = 1/(x + p + q)`

Solve x(x + 1) + (x + 2)(x + 3) = 42

Solve `1/(x - 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)`

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

`(m - 3)x^2 - 4x + 1 = 0`

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

`3x^2 + 12x + (m + 7) = 0`

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

`x^2 - (m + 2)x + (m + 5) = 0`

Without solving the following quadratic equation Find the value of p for which the roots are equal

`px^2 - 4x + 3 = 0`

Without solving the following quadratic equation, find the value of m for which the given equation has equation has real and equal roots.

`x^2 + 2(m - 1)x + (m + 5) = 0`

#### Exercise 5(F) [Page 67]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 5 Quadratic Equations Exercise 5(F) [Page 67]

Solve :

(x+5)(x-5)=24

Solve :

`3x^2 - 2sqrt6x + 2 = 0`

Solve :

`3sqrt(2x^2) - 5x - sqrt2 = 0`

Solve :

`2x - 3 = sqrt(2x^2 - 2x + 21)`

One root of the quadratic equation `8x^2 + mx + 15 = 0 is 3/4` Find the value of m. Also, find the other root of the equation.

If p -15 = 0 and `2x^2 + px + 25 = 0`;find the values of x.

Find the solution of the equation `2x^2 - mx - 25n = 0` if m + 5 = 0 and n - 1 = 0

If m and n are roots of the equation `1/x - 1/(x - 2) = 3` where x ≠ 0 and x ≠ 2; find m × n.

Solve, using formula :

`x^2 + x - (a + 2) (a + 1) = 0`

Solve the quadratic equation `8x^2 - 14x + 3 = 0`

(i) When `"x" in "I`(integers)

(ii) When `"x" in "Q"`(rational numbers)

Find the value of m for which the equation `(m + 4)x^2 + ( m + 1)x + 1 = 0` has real and equal roots.

Find the values of m for which equation `3x^2 + mx + 2 = 0` has equal roots. Also, find the roots of the given equation.

Find the value of k for which equation `4x^2 + 8x - k = 0` has real roots.

Find, using quadratic formula, the roots of the following quadratic equations, if they exist

`3x^2 - 5x + 2 = 0`

Find, using quadratic formula, the roots of the following quadratic equations, if they exist

`x^2 + 4x + 5 = 0`

Solve : `1/(18 - x) - 1/(18 + x) = 1/24` and x > 0.

Solve : `( x - 10) (1200/x + 2) = 1260` and x < 0.

## Chapter 5: Quadratic Equations

## Selina solutions for Concise Mathematics Class 10 ICSE chapter 5 - Quadratic Equations

Selina solutions for Concise Mathematics Class 10 ICSE chapter 5 (Quadratic Equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Concise Mathematics Class 10 ICSE solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Concise Mathematics Class 10 ICSE chapter 5 Quadratic Equations are Quadratic Equations, Solutions of Quadratic Equations by Factorization, Nature of Roots.

Using Selina Class 10 solutions Quadratic Equations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

Get the free view of chapter 5 Quadratic Equations Class 10 extra questions for Concise Mathematics Class 10 ICSE and can use Shaalaa.com to keep it handy for your exam preparation