Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 10

EASY

11th ICSE

IMPORTANT

Earn 100

If the roots of the equation $(c^{2} - a b) x^{2} - 2 (a^{2} - b c) x + (b^{2} - a c) = 0$ are equal, then prove that either $a = 0$ or $a^{3} + b^{3} + c^{3} = 3 a b c$ .

Important Questions on Quadratic Equations

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 11

Find the quadratic equation with rational coefficients one of whose roots is

\frac{3 + \sqrt{5}}{2 - \sqrt{5}}

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 12

If

α, β

are the roots of

x^{2} - p x + q = 0

, find the quadratic equation with roots

\frac{1}{p α - q}, \frac{1}{p β - q}

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 13

If

α, β

are the roots of

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

, find the quadratic equation with roots

α + \frac{1}{α}, β + \frac{1}{β}

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 14

If the sum of the roots of the equation

x^{2} - p x + q = 0

is

m

times their difference, then prove that

p^{2} (m^{2} - 1) = 4 m^{2} q

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 15

If the roots of the equation

(x - a) (x - b) - k = 0

are

c & d

, then prove that the roots of the equation

(x - c) (x - d) + k = 0

are

a & b

.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 16

Determine the values of

a

for which the equation

x^{2} - 2 (a + 1) x + 4 = 0

has real and distinct roots.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 16

Determine the values of

a

for which the equation

x^{2} - 2 (a + 1) x + 4 = 0

has equal roots.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>CHAPTER TEST>Q 17

Determine the values of

m

for which the equation

x^{2} - 2 m x + 8 m - 15 = 0

has equal roots.