show that $|x_1 -x_2|=\frac{\sqrt{\Delta}}{|a|}$, where $\Delta$ is the discriminant and $x_1,x_2$ the roots of a second degree polynomial equation

Question

Suppose that $P(x)=ax^2+bx+c, a,b,c\in\mathbb{R}, a\not=0$ has two real roots $x_1,x_2$. Show that $|x_1-x_2|=\frac{\sqrt{\Delta}}{|a|}$, where $\Delta$ is the discriminant.

Answer 1

Hint: $$|x_1-x_2|=\sqrt{(x_1+x_2)^2-4x_1x_2}$$ Now use the sum and product of roots conditions.