# What are the zeros of the function f(x)= 3x^2-3x-6?

Feb 9, 2017

$x = - 1$ and $x = 2$

#### Explanation:

Step 1. Factor out the function you were given

$f \left(x\right) = 3 {x}^{2} - 3 x - 6$
$\text{ } = 3 \left({x}^{2} - x - 2\right)$ ...factor out $3$, common to all three terms
$\text{ } = 3 \left(x + 1\right) \left(x - 2\right)$ ...identify a factorization of the polynomial

Step 2. Set the factored function equal to zero and solve

$3 \left(x + 1\right) \left(x - 2\right) = 0$

• $3$ is not zero
• $\left(x + 1\right) = 0$ when $x = - 1$
• $\left(x - 2\right) = 0$ when $x = 2$

Step 3. Verify these roots are zeros of the function by graphing

Feb 9, 2017

$x = - 1 , x = 2$

#### Explanation:

The zeros of f(x) are the values of x which make f(x) = 0

$\text{solve } 3 {x}^{2} - 3 x - 6 = 0$

$\Rightarrow 3 \left({x}^{2} - x - 2\right) = 0 \leftarrow \text{ common factor of 3}$

$\Rightarrow 3 \left(x - 2\right) \left(x + 1\right) = 0 \leftarrow \text{ factorise quadratic}$

$x - 2 = 0 \Rightarrow x = 2 \leftarrow \text{ is a zero}$

$x + 1 = 0 \Rightarrow x = - 1 \leftarrow \text{ is a zero}$