Question

How do you find the discriminant and how many solutions does `x^2 + 25 = 0` have?

Answer 1

This equation has no solutions.

We can see it in three ways:

1. it a sum of a quantity (`x^2`) that is positive or zero and a quantity (`25`) positive, so it could never be zero;
2. if you write the equation in this way: `x^2=-25`, you can see that a quantity positive or zero could never be negative;
3. if you find the discriminator `Delta=b^2-4ac=0^2-4*1*25=-100<0`, so the equation is impossible.