# How do you find the value of the discriminant and determine the nature of the roots 9m^2+6m+6=5?

Apr 16, 2018

 color(indigo)(D = 0, " and has ONE REAL ROOT, " m = -1/3

#### Explanation:

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

$9 {m}^{2} + 6 m + 6 = 5$

$9 {m}^{2} + 6 m + 6 - 5 = 0$

$9 {m}^{2} + 6 {m}_{+} 1 = 0$

$\text{here } a = 9 , b = 6 , c = 1$

$\therefore D = {b}^{2} - 4 a c = {6}^{2} - \left(4 \cdot 9 \cdot 1\right) = 36 - 36 = 0$

$\text{Hence " color(indigo)(D = 0, " and has ONE REAL ROOT, } m = - \frac{1}{3}$