Is there any real value of 'a' for which the equation x2 + 2x + (a2 +

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

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

Answer»

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.