Question

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

Answer 1

Let quadratic equation has real roots.

Here,

As we know that

Putting the value of , we get
$$\begin{gathered} D={\left(2\right)}^2-4\times 1\times \left(a^2+1\right) \\ =4-4\left(a^2+1\right) \\ =-4a^2 \end{gathered}$$

The given equation will have equal roots, if

i.e. $$\begin{gathered} -4a^2>0 \\ \Rightarrow a^2<0 \end{gathered}$$

which is not possible, as the square of any number is always positive.

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