Find the value of x, for the following: [1, x, 1]

Question

Find the value of x, for the following:

\(\begin{bmatrix} 1 & x & 1 \ \\ \end{bmatrix}\) \(\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix}\) \(\begin{bmatrix} 1 \\ 2 \\ x \end{bmatrix}=\) 0

Answer 1

We have

\(\begin{bmatrix} 1 & x & 1 \ \\ \end{bmatrix}\) \(\begin{bmatrix} 7+2x \\ 12+x \\ 21+2x \end{bmatrix}\) = 0

⇒ 7 + 2x + 12x + x² + 21 + 2x = 0

⇒ x² + 16x + 28 = 0

⇒ (x + 14) (x + 2) = 0

Either x+ 14 = 0 ⇒ x = - 14

or x + 2 = 0 ⇒ x = - 2