# What is the discriminant of 2x^2 + x - 1 = 0 and what does that mean?

Jul 26, 2015

Solve 2x^2 + x - 1 = 0

#### Explanation:

$D = {d}^{2} = {b}^{2} - 4 a c = 1 + 8 = 9$ --> $d = \pm 3$
This means there are 2 real roots (2 x-intercepts)
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} .$
$x = - \frac{1}{4} \pm \frac{3}{4}$ --> x = -1 and $x = \frac{1}{2}$

Jul 26, 2015

The discriminant is $9$.

A positive discriminant means that there are two real roots (x-intercepts).

Also, since the discriminant is a perfect square, the two roots are rational.

#### Explanation:

$2 {x}^{2} + x - 1 = 0$ is an quadratic equation in the form of $a {x}^{2} + b x + c$, where $a = 2 , b = 1 , \mathmr{and} c = - 1$.

The formula for the discriminant, $\text{D}$, comes from the quadratic formula, $x = \frac{- b \pm \sqrt{\textcolor{red}{{b}^{2} - 4 a c}}}{2 a}$ .

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

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

$\text{D} = 1 + 8$ =

$\text{D} = 9$

A positive discriminant means that there are two real roots (x-intercepts).

Since the discriminant is a perfect square, the two roots are also rational.