# How do use the discriminant to find all values of c for which the equation 2x^2+5x+c=0 has two real roots?

Feb 21, 2017

I tried this:

#### Explanation:

We need the discriminant to be greater then zero to have two different real roots (if it is equal to zero you'll have two coincident real roots). So we need:

$\Delta = {b}^{2} - 4 a c > 0$

where we use the convention for the general form of our equation where:
$a {x}^{2} + b x + c = 0$

we get:

$\Delta = {5}^{2} - 4 \left(2 c\right) > 0$
$25 - 8 c > 0$

rearranging:

$8 c < 25$
and
$c < \frac{25}{8}$

You can test your result by setting:

$c = \frac{25}{8}$
it'll give you $\Delta = 0$

$c = \frac{25}{8} - 1$
it'll give you $\Delta = 8$

$c = \frac{25}{8} + 1$
it'll give you $\Delta = - 8$