CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 6

MEDIUM

10th CBSE

IMPORTANT

Earn 100

Find the value(s) of $k$ for which following equation has equal roots: $x^{2} + k (2 x + k - 1) + 2 = 0$

Important Questions on Quadratic Equations

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 7

Find that non-zero value of

k

, for which the quadratic equation

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

has equal roots. Hence find the roots of the equation.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 8

Find the non-zero value of

k

, for which the quadratic equation

(3 k + 1) x^{2} + 2 (k + 1) x + 1 = 0

has equal roots. Hence, find the roots of the equation.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 9

If

- 5

is a root of the quadratic equation

2 x^{2} + p x - 15 = 0

and the quadratic equation

p (x^{2} + x) + k = 0

has equal roots, find the value of

k

.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 10

If

- 2

is a root of the quadratic equation

3 x^{2} + 7 x + p = 0

, find the values of

k

for which the roots of the equation

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

are equal.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 11

If

a d \neq b c

then prove that the equation

(a^{2} + b^{2}) x^{2} + 2 (a c + b d) x + (c^{2} + d^{2}) = 0

has no real roots.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 12

Determine the value(s) of

p

for which quadratic equation

2 x^{2} + 3 x + p = 0

has real roots.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 13

In the quadratic equation

k x^{2} - 6 x - 1 = 0

, determine the values of

k

for which the equation does not have real roots.

EASY

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 4 - Quadratic Equations>Exercise 4.4>Q 14

For what value of m will the equation

2 m x^{2} - 2 (1 + 2 m) x + (3 + 2 m) = 0

have real but distinct roots? When will the roots be equal?