Q. 73.8( 6 Votes )

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.


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