Read the statements carefully.Statement - I : The quadratic equation a

1.	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» 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.

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»

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.