# How to use the discriminant to find out what type of solutions the equation has for x^2-4x+10=0?

May 17, 2015

The general formula for the solutions of a quadratic equation $a {x}^{2} + b x + c$ is:

${x}_{1 , 2}$ = $\frac{- b \pm \sqrt{\Delta}}{2 a}$, where the discriminant $\Delta$ = ${b}^{2} - 4 a c$.

We calculate the value of the discriminant for our particular equation
(${x}^{2} - 4 x + 10$):

$\Delta$ = $16 - 4 \cdot 1 \cdot 10$ = $- 22$

As the discriminant $\Delta$$<$$0$, our equation does not have solutions in the set of real numbers.