Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 8

EASY

10th CBSE

IMPORTANT

Earn 100

Find the values of $k$ for which the quadratic equation $(3 k + 1) x^{2} + 2 (k + 1) x + 1 = 0$ has real and equal roots.

Important Questions on Quadratic Equations

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 8

Find the value of $k$ for which the equation

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

has real and equal roots.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 9

Find the value of

p

for which the quadratic equation

(2 p + 1) x^{2} - (7 p + 2) x + (7 p - 3) = 0

has real and equal roots.

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 10

Find the values of $p$ for which the quadratic equation

(p + 1) x^{2} - 6 (p + 1) x + 3 (p + 9) = 0, p \neq - 1

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

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 11

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

.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 12

If

3

is a root of the quadratic equation

x^{2} - x + k = 0

find the value of

p

so that the roots of the equation

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

are equal.

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 13

If

- 4

is a root of the equation

x^{2} + 2 x + 4 p = 0

find the value of

k

for the which the quadratic equation

x^{2} + p x (1 + 3 k) + 7 (3 + 2 k) = 0

has equal roots.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 14

If the quadratic equation

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

has equal roots, prove that

c^{2} = a^{2} (1 + m^{2})

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 15

If the roots of the quadratic equation

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

are real and equal, show that either

a = 0

or

(a^{3} + b^{3} + c^{3} = 3 a b c)