# How do you find all the roots of f(x) = 3x^2 + 18x + 27?

Aug 13, 2016

$f \left(x\right)$ has zero $x = - 3$ of multiplicity $2$

#### Explanation:

$f \left(x\right) = 3 {x}^{2} + 18 x + 27$

$= 3 \left({x}^{2} + 6 x + 9\right)$

$= 3 \left({x}^{2} + 2 \left(3\right) x + {3}^{2}\right)$

$= 3 {\left(x + 3\right)}^{2}$

So the zeros of $f \left(x\right)$ are both $- 3$, i.e. $x = - 3$ is a zero with multiplicity $2$.