# How to use the discriminant to find out how many real number roots an equation has for x^2 - 5x + 7 = 0?

${x}^{2} - 5 x + 7$ is of the form $a {x}^{2} + b x + c$, with $a = 1$, $b = - 5$ and $c = 7$.
$\Delta = {b}^{2} - 4 a c$
$= {\left(- 5\right)}^{2} - \left(4 \times 1 \times 7\right) = 25 - 28 = - 3$
Being negative, we can deduce that ${x}^{2} - 5 x + 7 = 0$ has no real roots (it has two distinct complex roots).