Question

Is there any real value of 'a' for which the equation x²+ 2x + (a² + 1) = 0 has real roots?

Answer 1

SOLUTION :  

Given : x² + 2x + (a² + 1) = 0

On comparing the given equation with ax² + bx + c = 0  

Here, a = 1 , b = 2 , c = (a² + 1)

D(discriminant) = b² – 4ac

D = 2² - 4 × 1 × (a² + 1)

D = 4 - 4(a² + 1)

D = 4 - 4a² - 4  

D = - 4a²  

D = - 4a² < 0

For real roots , D ≥ 0

Since, D < 0 , so given equation has no real value of 'a' .

Hence, there is no real value of ‘a’ for which the given equation has real roots.

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Answer:

Thus, No, there is no any real value of a for which the given equation has real roots.