What is the discriminant of x^2 + 5x + 7 = 0 and what does that mean?

Jul 27, 2015

The discriminant is $- 3$, which means there are two complex roots.

Explanation:

${x}^{2} + 5 x + 7 = 0$ is a quadratic equation. The general form of a quadratic equation is ${a}^{2} + b x + c$, where $a = 1 , b = 5 , \mathmr{and} c = 7$.
The discriminant, $\text{D}$, comes from the quadratic formula in which $x = \frac{- b \pm \sqrt{\textcolor{red}{{b}^{2} - 4 a c}}}{2 a}$ .

$\text{D} = {b}^{2} - 4 a c$ =

$\text{D} = {5}^{2} - 4 \left(1\right) \left(7\right)$ =

$\text{D} = 25 - 28$ =

$\text{D} = - 3$

A negative discriminant means there are two complex roots (x-intercepts).