Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 2

MEDIUM

10th CBSE

IMPORTANT

Earn 100

If $a$ and $b$ are distinct real numbers, show that the quadratic equations
$2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$ has no real roots.

Important Questions on Quadratic Equations

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 3

Show that the roots of the equation

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

are real for all real values of

p

and $q$

EASY

10th CBSE

IMPORTANT

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

Find the values of

k

for whcih the roots of the quadratic equation

3 x^{2} + 2 k x + 27

real and equal.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 5

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.

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 6

For what values of

p

are the roots of the equation

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

real and equal?

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 7

Find the nonzero value of

k

for which the roots of the quadratic equation

9 x^{2} - 3 k x + k = 0

are real and equal.

EASY

10th CBSE

IMPORTANT

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

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.

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.