Question

Read the statements carefully.

Statement - I : The quadratic equation ax² + bx + c = 0 has two distinct real roots, if b² - 4ac > 0.

Statement - II : The quadratic equation 2(a² + b²)x² + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.

(A) Both Statement - I and Statement - II are true.

(B) Statement - I is true but Statement - II is false.

(C) Statement - I is false but Statement - II is true.

(D) Both Statement - I and Statement - II are false.

Answer 1

The correct option is: (C) Statement - I is false but Statement - II is true.

Explanation:

Statement - I is false, since the quadratic equation ax² + bx + c = 0 has two distinct real roots, if b² - 4ac > 0.

Also, given equation is

2(a² + b²)x² + 2(a + b)x + 1 = 0

D = b² - 4ac = (2(a + b))² - 4(2a² + 2b²)(1)

= 4a² + 4b² + 8ab - 8a² - 8b²

= 4a² - 4b² + 8ab= 4(a - b)² < 0

.'. Given equation has no real roots. Hence, statement - II is true.