# How to use the discriminant to find out how many real number roots an equation has for 8b^2 - 6b + 3 = 5b^2?

Apr 16, 2018

color(crimson)("The given equation has TWO REAL ROOTS"

#### Explanation:

For a given quadratic equation in the standard form $a {x}^{2} + b x + c$,

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

$8 {b}^{2} - 6 b + 3 = 5 {b}^{2}$

$8 {b}^{2} - 5 {b}^{2} - 6 b + 3 = 0 , \text{ making R H S = 0}$

$3 {b}^{2} - 6 b + 3 = 0$

:. D = b^2 - 4 a c = (-6)^2 - (4 * 3 * 3) = 36 - 24 = 12, color(green)(" which is " > 0 " (Positive)"

Hence color(crimson)("The given equation has TWO REAL ROOTS"