Is there any real value of 'a' for which the equation

x² + 2x + (a² + 1) = 0 has real roots?

A quadratic equation has two real roots if discriminant = 0

For the given equation, we have:

d = b² – 4 a c

d = (2)² – 4 (1) (a² + 1)

d = 4 – 4(a² + 1)

d = 4(1 – a² – 1)

d = – 4a²

Now, D = 0 when a = 0. So, the equation will have real and equal roots if a = 0. And for all other values of a, the equation will have no real roots.

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