# How do you find the zeros of f(x)=2x^2+x-3?

Apr 5, 2017

${x}_{1} = 1 \mathmr{and} {x}_{2} = - \frac{3}{2}$

#### Explanation:

Factor the equation $f \left(x\right)$ (I'll use decomposition),

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

Factor,

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

Simplify,

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

Let $f \left(x\right) = 0 ,$

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

The values of x that make this statement above true (zeros), are

${x}_{1} = 1 \mathmr{and} {x}_{2} = - \frac{3}{2}$