# Question #957bb

May 24, 2016

no real roots

#### Explanation:

To determine the number of real roots, find the discriminant of the given equation.

The discriminant is given as:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} D = {b}^{2} - 4 a c \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$a = 1 \textcolor{w h i t e}{X} , \textcolor{w h i t e}{X} b = 3 \textcolor{w h i t e}{X} , \textcolor{w h i t e}{X} c = 9$

Plugging in the numbers,

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

$D = {\left(3\right)}^{2} - 4 \left(1\right) \left(9\right)$

$D = 9 - 36$

$D = - 27$

Since the discriminant is less than $0$, there are no real roots.