Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 20

EASY

11th ICSE

IMPORTANT

Earn 100

Find the condition that one of the roots of the equation $a x^{2} + b x + c = 0$ is positive and the other is negative.

Important Questions on Quadratic Equations

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 21

For what value of

a

one of the roots of the equation

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

is double the other.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 21

Determine

k

if one of the roots of the equation

k (x - 1)^{2} = 5 x - 7

is double the other.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 21

Find the values of

k

for which the roots

α, β

of the equation

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

satisfy the relation

2 α + 3 β = 20

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 21

Solve the equation

x^{2} + p x + 45 = 0

if the square of the difference of the roots is

144

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 22

Find the possible values of

a

, if one root of

8 x^{2} - 6 x + a = 0

is square of the other.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 23

Find the condition if the equations

a x^{2} + b x + c = 0

and

a^{'} x^{2} + b^{'} x + c^{'} = 0

have reciprocal roots.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 24

If the equations

2 x^{2} + k x - 5 = 0

and

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

have a common root, find possible values of

k

and also find the common root.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 6 - Quadratic Equations>EXERCISE 6.4>Q 25

If the equations

x^{2} - 11 x + k = 0

and

x^{2} - 14 x + 2 k = 0

have a common root, find possible values of

k