# What are the zeros of the trinomial 4x^2-17x+4?

Oct 30, 2017

$x = \frac{1}{4} , x = 4$

#### Explanation:

$\text{factorise the trinomial and equate to zero}$

$\text{the factors of + 16 which sum to - 17 are - 16 and - 1}$

$\Rightarrow 4 {x}^{2} - 16 x - x + 4$

$= \textcolor{red}{4 x} \left(x - 4\right) \textcolor{red}{- 1} \left(x - 4\right) \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$= \left(x - 4\right) \left(\textcolor{red}{4 x - 1}\right)$

$\Rightarrow \left(x - 4\right) \left(4 x - 1\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x - 4 = 0 \Rightarrow x = 4$

$4 x - 1 = 0 \Rightarrow x = \frac{1}{4}$