# How do you find the value of the discriminant and determine the nature of the roots r^2+5r+2=0?

Apr 13, 2017

$\Delta = 17$

$\text{ roots are real and unequal}$

#### Explanation:

For any quadratic $\text{ } a {x}^{2} + b x + c = 0$

the discriminant is given by$\text{ } \Delta = {b}^{2} - 4 a c$

the nature of the roots is determined by the following;

$\Delta > 0 \implies \text{roots are real and unequal}$

$\Delta = 0 \implies \text{roots are real and equal}$

$\Delta < 0 \implies \text{roots are imaginary}$

for $\text{ } {r}^{2} + 5 r + 2 = 0$

$a = 1 , b = 5 , c = 2$

$\Delta = {5}^{2} - 4 \times 1 \times 2$

$\Delta = 25 - 8 = 17 > 0$

$\therefore \text{ roots are real and unequal}$