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

Find which of the following equations are quadratic:

(3x – 1)² = 5(x + 8)

Find which of the following equations are quadratic:

5x² – 8x = –3(7 – 2x)

Find which of the following equations are quadratic:

(x – 4)(3x + 1) = (3x – 1)(x + 2)

Find which of the following equations are quadratic:

x² + 5x – 5 = (x – 3)²

Find which of the following equations are quadratic:

7x³ – 2x² + 10 = (2x – 5)²

Find which of the following equations are quadratic:

(x – 1)² + (x + 2)² + 3(x + 1) = 0

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

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

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

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

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

Without solving, comment upon the nature of roots of the following equation:

7x² – 9x + 2 = 0

Without solving, comment upon the nature of roots of the following equation: 

6x² – 13x + 4 = 0

Without solving, comment upon the nature of roots of the following equation:

25x² − 10x + 1 = 0

Without solving, comment upon the nature of roots of the following equation: 

`x^2 + 2sqrt(3)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 equation: 

2x² + 8x + 9 = 0

Find the value of ‘p’, if the following quadratic equation have equal roots:

4x² – (p – 2)x + 1 = 0

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

x² + (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)x² – (5 + m)x + 16 = 0

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

Solve equation using factorisation method:

x² – 10x – 24 = 0

Solve equation using factorisation method:

x² – 16 = 0

Solve equation using factorisation method:

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

Solve equation using factorisation method:

x(x – 5) = 24

Solve equation using factorisation method:

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

Solve equation using factorisation method:

`6/x = 1 + x`

Solve equation using factorisation method:

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

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(x² – 6) = 3(x – 4)

Solve equation using factorisation method:

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

Solve equation using factorisation method:

x² – (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 the equation using the factorisation method:

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

Solve equation using factorisation method:

2x² – 9x + 10 = 0, when:

1. x ∈ N
2. 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/(2x + 1)`

Solve equation using factorisation method:

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

Solve equation using factorisation method:

`(1 + 1/(x+1))(1-1/(x-1)) = 7/8`

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 x² + ax – 6 = 0.

Find the value of x, if a + 7 = 0; b + 10 = 0 and 12x² = 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 6x² – 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 x² - 3x +2=0 or not.

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

Find the value of m.

If x = −3 and x = `2/3` are solutions of quadratic equation mx² + 7x + n = 0, find the values of m and n.

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.

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 x²+px+q=0
then find the values of p and q

Solve the following equation using the formula:

x² – 6x = 27

Solve the following equation using the formula:

x² – 10x + 21 = 0

Solve the following equation using the formula: 

x² + 6x – 10 = 0

Solve the following equation using the formula: 

x² + 2x – 6 = 0

Solve the following equation using the formula: 

3x² + 2x – 1 = 0

Solve the following equation using the formula:

2x² + 7x + 5 = 0

Solve the following equation using the formula: 

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

Solve the following equation using the formula: 

`1/15x^2 + 5/3 = 2/3x` 

Solve the following equation using the formula: 

`x^2 - 6 = 2sqrt(2)x` 

Solve the following equation using the formula: 

`4/x - 3 = 5/(2x + 3)` 

Solve the following equation using the formula: 

`(2x + 3)/(x + 3) = (x + 4)/(x + 2)` 

Solve the following equation using the formula: 

`sqrt(6)x^2 - 4x - 2sqrt(6) = 0` 

Solve the following equation using the formula: 

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

Solve the following equation using the formula: 

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

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

x² – 8x + 5 = 0

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

5x² + 10x – 3 = 0

Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:

2x² – 10x + 5 = 0

Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:

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

Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:

4x² – 5x – 3 = 0

Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:

x² – 3x – 9 = 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 the following equation for x and give, in the following case, your answer correct to 3 decimal places:

3x² – 12x – 1 = 0

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

x² – 16x + 6 = 0

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

2x² + 11x + 4 = 0

Solve :

x⁴ - 2x² - 3 = 0

Solve : x⁴ - 10x² +9 =0

Solve:

(x² – x)² + 5(x² – x) + 4 = 0

Solve:

(x² – 3x)² – 16(x² – 3x) – 36 = 0

Solve:

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

Solve: 

`((2x -3)/(x - 1)) - 4((x - 1)/(2x - 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 x² –  3(x + 3) = 0; Give your answer correct to two significant figures.

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`

Show that one root of the quadratic equation x² + (3 – 2a)x – 6a = 0 is –3. Hence, find its other root.

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

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

Solve:

2x⁴ – 5x² + 3 = 0

Solve: x⁴ – 2x² – 3 = 0.

Solve:

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

Solve: `(x^2 + 1/x^2) - 3(x - 1/x) - 2 = 0`

Solve:

(x² + 5x + 4)(x² + 5x + 6) = 120

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

3x² – x – 7 =0

Solve:

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

Solve : x² – 11x – 12 =0; when x ∈ N

Solve x² – 4x – 12 =0; when x ∈ I

Solve  2x² – 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 the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:

(m – 3)x² – 4x + 1 = 0

For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also find the solution of the equation:

3x² + 12x + (m + 7) = 0

For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:

x² – (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`

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 8x² + mx + 15 = 0 is `3/4`. Find the value of m. Also, find the other root of the equation.

If p – 15 = 0 and 2x² + px + 25 = 0; find the values of x.

Find the solution of the equation 2x² – 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:

x² + x – (a + 2)(a + 1) = 0

Solve the quadratic equation 8x² – 14x + 3 = 0

1. When x ∈ I (integers)
2. When x ∈ Q (rational numbers)

Find the value of m for which the equation (m + 4)x² + (m + 1)x + 1 = 0 has real and equal roots.

Find the values of m for which equation 3x² + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.

Find the value of k for which equation 4x² + 8x – k = 0 has real roots.

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

3x² – 5x + 2 = 0

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

x² + 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