# How to use the discriminant to find out how many real number roots an equation has for 2m^2 - m - 6 = 0?

Mar 26, 2018

#### Explanation:

The discriminant, ($\Delta$), is derived from quadratic equation:
$x = \frac{{b}^{2} \pm \left(\sqrt{{b}^{2} - 4 a c}\right)}{2 a}$

Where $\Delta$ is the expression beneath the root sign, hence:
The discriminant ($\Delta$) =${b}^{2} - 4 a c$

If $\Delta$>0 there are 2 real solutions (roots)
If $\Delta = 0$ there is 1 repeated solution (root)
If 0>$\Delta$ then the equations has no real solutions (roots)

In this case $b = - 1$, $c = - 6$ and $a = 2$
${b}^{2} - 4 a c = {\left(- 1\right)}^{2} - 4 \left(2\right) \left(- 6\right) = 49$

So your equation has two real solutions as $\Delta$>0. Using the quadratic formula these turn out to be:

$x = \frac{1 \pm \left(\sqrt{49}\right)}{4}$

${x}_{1} = 2$

${x}_{2} = \left(- \frac{6}{4}\right) = - 1.5$