#### 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

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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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