# How do you find the values of x given [(x,4,1)][(2,1,0), (1, 0, 2), (0, 2, 4)][(x), (-7), (5/4)]=0?

Nov 25, 2017

$x = \frac{1}{2} \text{ }$ or $\text{ } x = 1$

#### Explanation:

$\left(0\right) = \left(\left(x , 4 , 1\right)\right) \left(\begin{matrix}2 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & 4\end{matrix}\right) \left(\begin{matrix}x \\ - 7 \\ \frac{5}{4}\end{matrix}\right)$

$\textcolor{w h i t e}{\left(0\right)} = \left(\left(2 x + 4 , x + 2 , 12\right)\right) \left(\begin{matrix}x \\ - 7 \\ \frac{5}{4}\end{matrix}\right)$

$\textcolor{w h i t e}{\left(0\right)} = \left(2 {x}^{2} + 4 x - 7 x - 14 + 15\right)$

$\textcolor{w h i t e}{\left(0\right)} = \left(2 {x}^{2} - 3 x + 1\right)$

$\textcolor{w h i t e}{\left(0\right)} = \left(\left(2 x - 1\right) \left(x - 1\right)\right)$

So:

$x = \frac{1}{2} \text{ }$ or $\text{ } x = 1$