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Selina solutions for Concise Mathematics Class 10 ICSE chapter 5 - Quadratic Equations [Latest edition]

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Concise Mathematics Class 10 ICSE - Shaalaa.com

Chapter 5: Quadratic Equations

Exercise 5(A)Exercise 5(B)Exercise 5(C)Exercise 5(D)Exercise 5(E)Exercise 5(F)

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

Exercise 5(A) | Q 1.1 | Page 54

Find which of the following equation are quadratic:

(3x - 1)2 = 5(x + 8)

Exercise 5(A) | Q 1.2 | Page 54

Find which of the following equation are quadratic:

5x2 - 8x = -3(7 - 2x)

Exercise 5(A) | Q 1.3 | Page 54

Find which of the following equation are quadratic:

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

Exercise 5(A) | Q 1.4 | Page 54

Find which of the following equation are quadratic:

x2 + 5x - 5 = (x - 3)2

Exercise 5(A) | Q 1.5 | Page 54

Find which of the following equations are quadratic:

7x3 - 2x2 + 10 = (2x - 5)2

Exercise 5(A) | Q 1.6 | Page 54

Find which of the following equation are quadratic:

(x - 1)2 + (x + 2)2 + 3(x +1) = 0

 

Exercise 5(A) | Q 2.1 | Page 54

Is x = 5 a solution of the quadratic equation x2 - 2x - 15 = 0?

Exercise 5(A) | Q 2.2 | Page 54

Is x = -3 a solution of the quadratic equation 2x2 - 7x + 9 = 0?

Exercise 5(A) | Q 3 | Page 54

If `sqrt (2/3)` is a solution of equation 3x2 + mx + 2 = 0, find the value of m.

Exercise 5(A) | Q 4 | Page 54

`2/3`and 1 are the solutions of equation mx2 + nx + 6 = 0. Find the values of m and n.

Exercise 5(A) | Q 5 | Page 54

If 3 and -3 are the solutions of equation ax2 + bx - 9 = 0. Find the values of a and b.

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

Exercise 5(B) | Q 1.1 | Page 56

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

 7x2 – 9x + 2 = 0

Exercise 5(B) | Q 1.2 | Page 56

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

6x2 – 13x + 4 = 0   

Exercise 5(B) | Q 1.3 | Page 56

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

`25x^2 − 10x + 1 = 0 `

Exercise 5(B) | Q 1.4 | Page 56

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

Exercise 5(B) | Q 1.5 | Page 56

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

`"x"^2 – "ax" – "b"^2 = 0`

Exercise 5(B) | Q 1.6 | Page 56

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

`2"x"^2 + 8"x" + 9 = 0` 

Exercise 5(B) | Q 2.1 | Page 56

Find the value of p, if the following quadratic equation has equal roots: 4x2 – (p – 2)x + 1 = 0

Exercise 5(B) | Q 2.2 | Page 56

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

x2 + (p - 3)x + p = 0

Exercise 5(B) | Q 3 | Page 56

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

Exercise 5(B) | Q 4 | Page 56

Find the value of m, if the following equation has equal roots : (m – 2)x2 – (5+m)x +16 =0

Exercise 5(B) | Q 5 | Page 56

Find the value of k for which the equation 3x2- 6x + k = 0 has distinct and real roots.

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

Exercise 5(C) | Q 1 | Page 59

Solve equation using factorisation method:

x2 - 10x - 24 = 0

Exercise 5(C) | Q 2 | Page 59

Solve equation using factorisation method:

x2 - 16 = 0

Exercise 5(C) | Q 3 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 4 | Page 59

Solve equation using factorisation method:

x (x - 5) = 24

Exercise 5(C) | Q 5 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 6 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 7 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 8 | Page 59

Solve equation using factorisation method:

x + `1/"x"` = 2.5

Exercise 5(C) | Q 9 | Page 59

Solve equation using factorisation method:

(2x - 3)2 = 49

Exercise 5(C) | Q 10 | Page 59

Solve equation using factorisation method:

2(x2 - 6) = 3(x - 4)

Exercise 5(C) | Q 11 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 12 | Page 59

Solve equation using factorisation method:

x2 - (a + b) x + ab = 0

Exercise 5(C) | Q 13 | Page 59

Solve equation using factorisation method:

(x - 3)2 -4(x +3) -5 = 0

Exercise 5(C) | Q 14 | Page 59

Solve equation using factorisation method:

4(2x - 3)2 - (2x - 3) - 14 = 0

Exercise 5(C) | Q 15 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 16 | Page 59

Solve equation using factorisation method:

2x2 - 9x + 10 = 0, When

(i) x∈ N

(ii) x∈ Q

Exercise 5(C) | Q 17 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 18 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 19 | Page 59

Solve equation using factorisation method:

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

Exercise 5(C) | Q 21.1 | Page 59

Find the quadratic equation, whose solution set is :

{3,5}

Exercise 5(C) | Q 21.2 | Page 59

Find the quadratic equation, whose solution set is :

(-2,3}

Exercise 5(C) | Q 22.1 | Page 59

Solve:

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

Exercise 5(C) | Q 22.2 | Page 59

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

Exercise 5(C) | Q 23 | Page 60

Find the value of x, if a + 1=0 and x2 + ax - 6 =0.

Exercise 5(C) | Q 24 | Page 60

Find the value of x, if a + 7=0; b + 10=0 and 12x2 = ax - b.

Exercise 5(C) | Q 25 | Page 60

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

Exercise 5(C) | Q 26 | Page 60

Without solving the quadratic equation 6x2 – x – 2=0, find whether x = 2/3 is a solution of this equation or not.

Exercise 5(C) | Q 27 | Page 59

Determine whether x = -1 is a root of the equation x2 - 3x +2=0 or not.

Exercise 5(C) | Q 28 | Page 60

If x = `2/3` is a solution of the quadratic equation 7x2+mx - 3=0;

Find the value of m.

Exercise 5(C) | Q 29 | Page 60

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

Exercise 5(C) | Q 30 | Page 60

If quadratic equation x2 - (m + 1) x + 6=0 has one root as x =3;

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

Exercise 5(C) | Q 31 | Page 60

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.

Exercise 5(C) | Q 32 | Page 60

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

Exercise 5(C) | Q 33 | Page 60

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

Exercise 5(C) | Q 34 | Page 60

If -1 and 3 are the roots of x2+px+q=0
then find the values of p and q

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

Exercise 5(D) | Q 1.01 | Page 64

Solve the following equation using the formula

`x^2 - 6x = 27`

Exercise 5(D) | Q 1.02 | Page 64

Solve the following equation using the formula

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

Exercise 5(D) | Q 1.03 | Page 64

Solve each of the following equations using the formula: 

`x^2 + 6x – 10 = 0` 

Exercise 5(D) | Q 1.04 | Page 64

Solve each of the following equations using the formula: 

`x^2 + 2x – 6 = 0` 

Exercise 5(D) | Q 1.05 | Page 64

Solve each of the following equations using the formula: 

`3x^2 + 2x – 1 = 0`

Exercise 5(D) | Q 1.06 | Page 64

Solve the following equations using the formula

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

Exercise 5(D) | Q 1.07 | Page 64

Solve each of the following equations using the formula: 

`2/3x=-1/6x^2-1/3` 

Exercise 5(D) | Q 1.08 | Page 64

Solve each of the following equations using the formula: 

`1/15x^2+5/3=2/3x` 

Exercise 5(D) | Q 1.09 | Page 64

Solve each of the following equations using the formula: 

`x^2-6=2sqrt2x` 

Exercise 5(D) | Q 1.1 | Page 64

Solve each of the following equations using the formula: 

`4/x-3=5/(2x+3)` 

Exercise 5(D) | Q 1.11 | Page 64

Solve each of the following equations using the formula : 

`(2x+3)/(x+3)=(x+4)/(x+2)` 

Exercise 5(D) | Q 1.12 | Page 64

Solve each of the following equations using the formula: 

`sqrt6x^2-4x-2sqrt6=0` 

Exercise 5(D) | Q 1.13 | Page 64

Solve each of the following equations using the formula: 

`(2x)/(x-4)+(2x-5)/(x-3)=8 1/3` 

Exercise 5(D) | Q 1.14 | Page 64

Solve each of the following equations using the formula: 

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3` 

Exercise 5(D) | Q 2.1 | Page 64

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

x2 – 8x+5=0

Exercise 5(D) | Q 2.2 | Page 64

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

5x2 +10x – 3 =0

Exercise 5(D) | Q 3.1 | Page 64

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

2x2 – 10x +5=0

Exercise 5(D) | Q 3.2 | Page 64

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

Exercise 5(D) | Q 3.4 | Page 64

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

x2 – 3x – 9 =0

Exercise 5(D) | Q 3.5 | Page 64

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`

Exercise 5(D) | Q 4.1 | Page 64

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

3x2 – 12x – 1 =0

Exercise 5(D) | Q 4.2 | Page 64

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

x2 - 16 x +6= 0

Exercise 5(D) | Q 4.3 | Page 64

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

2x2 + 11x + 4= 0

Exercise 5(D) | Q 5.1 | Page 64

Solve :

x4 - 2x2 - 3 = 0

Exercise 5(D) | Q 5.2 | Page 64

Solve : x4 - 10x2 +9 =0

Exercise 5(D) | Q 6.1 | Page 64

Solve : (x2 – x)2 + 5(x2 – x)+ 4=0

Exercise 5(D) | Q 6.2 | Page 64

Solve :

(x2 - 3x)2 - 16(x2 - 3x) - 36 =0

Exercise 5(D) | Q 7.1 | Page 64

Solve:

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

Exercise 5(D) | Q 7.2 | Page 64

Solve: 

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

Exercise 5(D) | Q 7.3 | Page 64

Solve: 

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

Exercise 5(D) | Q 8 | Page 64

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

Exercise 5(D) | Q 9 | Page 64

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

Exercise 5(D) | Q 10 | Page 64

Solve for x using the quadratic formula. Write your answer correct to two significant figures.
(x – 1)2 – 3x + 4 = 0

Exercise 5(D) | Q 11 | Page 64

Solve the quadratic equation x2 -  3(x + 3) = 0; Give your answer correct two significant figures

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

Exercise 5(E) | Q 1 | Page 66

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

Exercise 5(E) | Q 2 | Page 66

Solve: (2x+3)= 81

Exercise 5(E) | Q 3 | Page 66

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

Exercise 5(E) | Q 3 | Page 67

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

Exercise 5(E) | Q 4 | Page 66

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

Exercise 5(E) | Q 5 | Page 66

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

Exercise 5(E) | Q 6 | Page 66

Solve: 2x4 – 5x² + 3 = 0

Exercise 5(E) | Q 7 | Page 66

Solve: x4 – 2x² – 3 = 0.

Exercise 5(E) | Q 8 | Page 66

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

Exercise 5(E) | Q 9 | Page 66

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

Exercise 5(E) | Q 11 | Page 66

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

Exercise 5(E) | Q 12.2 | Page 67

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

3x2 – x – 7 =0

Exercise 5(E) | Q 13 | Page 67

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

Exercise 5(E) | Q 14.1 | Page 67

Solve : x2 – 11x – 12 =0; when x ∈ N

Exercise 5(E) | Q 14.2 | Page 67

Solve x2 – 4x – 12 =0; when x ∈ I

Exercise 5(E) | Q 14.3 | Page 67

Solve  2x2 – 9x + 10 =0; when x ∈ Q

Exercise 5(E) | Q 15 | Page 67

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

Exercise 5(E) | Q 16 | Page 67

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

Exercise 5(E) | Q 17.1 | Page 67

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

Exercise 5(E) | Q 17.2 | Page 67

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

Exercise 5(E) | Q 18.1 | Page 67

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` 

Exercise 5(E) | Q 18.2 | Page 67

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`

Exercise 5(E) | Q 18.3 | Page 67

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`

Exercise 5(E) | Q 19 | Page 67

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

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

Exercise 5(E) | Q 20 | Page 67

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`

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

Exercise 5(F) | Q 1.1 | Page 67

Solve :
 (x+5)(x-5)=24
 

Exercise 5(F) | Q 1.2 | Page 67

Solve : 
`3x^2 - 2sqrt6x + 2 = 0`

Exercise 5(F) | Q 1.3 | Page 67

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

Exercise 5(F) | Q 1.4 | Page 67

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

Exercise 5(F) | Q 2 | Page 67

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. 

Exercise 5(F) | Q 4 | Page 67

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

Exercise 5(F) | Q 5 | Page 67

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

Exercise 5(F) | Q 6 | Page 67

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

Exercise 5(F) | Q 7 | Page 67

Solve, using formula : 
`x^2 + x - (a + 2) (a + 1) = 0`

Exercise 5(F) | Q 8 | Page 67

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

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

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

Exercise 5(F) | Q 9 | Page 67

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

Exercise 5(F) | Q 10 | Page 67

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

Exercise 5(F) | Q 11 | Page 67

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

Exercise 5(F) | Q 12.1 | Page 67

Find, using quadratic formula, the roots of the following quadratic equations, if they exist 
 `3x^2 - 5x + 2 = 0`

Exercise 5(F) | Q 12.2 | Page 67

Find, using quadratic formula, the roots of the following quadratic equations, if they exist
`x^2 + 4x + 5 = 0`

Exercise 5(F) | Q 13.1 | Page 67

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

Exercise 5(F) | Q 13.2 | Page 67

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

Chapter 5: Quadratic Equations

Exercise 5(A)Exercise 5(B)Exercise 5(C)Exercise 5(D)Exercise 5(E)Exercise 5(F)
Concise Mathematics Class 10 ICSE - Shaalaa.com

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.

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