# How do use the discriminant to find all values of b for which the equation 3x^2+bx+5=0 has one real root?

Apr 26, 2017

$b = \pm 2 \sqrt{15}$

#### Explanation:

The discriminant is

$\Delta = {b}^{2} - 4 a c = {b}^{2} - 4 \cdot 3 \cdot 5 = {b}^{2} - 60$

The discriminant will be null if the equation has one real root, then it must be:

${b}^{2} - 60 = 0$

that's

$b = \pm \sqrt{60} = \pm 2 \sqrt{15}$