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

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 $\Delta = {b}^{2} - 4 a c = {0}^{2} - 4 \cdot 1 \cdot 25 = - 100 < 0$, so the equation is impossible.