# How do you find all the zeros of f(x)=2x^2-7x-30?

Jun 24, 2016

Zeros: $x = - \frac{5}{2}$ and $x = 6$

#### Explanation:

$f \left(x\right) = 2 {x}^{2} - 7 x - 30$

Use an AC method:

Find a pair of factors of $A C = 2 \cdot 30 = 60$ which differ by $B = 7$.

The pair $12 , 5$ works.

Use that pair to split the middle term and factor by grouping:

$2 {x}^{2} - 7 x - 30$

$= 2 {x}^{2} - 12 x + 5 x - 30$

$= \left(2 {x}^{2} - 12 x\right) + \left(5 x - 30\right)$

$= 2 x \left(x - 6\right) + 5 \left(x - 6\right)$

$= \left(2 x + 5\right) \left(x - 6\right)$

Hence zeros $x = - \frac{5}{2}$ and $x = 6$