What is the discriminant of the equation x^ 2 + 4x – n^2= 0 ? And how many solutions does it have?

Answer

Discriminant for ax^2 + bx + c is b^2 – 4ac.

Thus, in our case,

Discriminant = 4^2 – 4*(1)(-n^2)
= 16 + 4n^2

Now, since n^2 is non-negative for any real n,
Thus, 16 + 4n^2 > 0 for all real values of n.

Hence, Discriminant > 0.

This means our quadratic equation above has two distinct roots. or you can say two distinct solutions.