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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
MCQ
Find the value of x, if $\begin{bmatrix}1&-1\\3&-5\end{bmatrix}=\begin{bmatrix}\text{x}&\text{x}^2\\3&-5\end{bmatrix}$ is:
  • ✓
    $\text{x}=2,-\frac{1}{3}$
  • B
    $\text{x}=-1,-\frac{1}{3}$
  • C
    $\text{x}=-2,-\frac{1}{3}$
  • D
    $\text{x}=0,-\frac{1}{3}$
✓

Answer

Correct option: A.
$\text{x}=2,-\frac{1}{3}$
Given that, $\begin{bmatrix}1&-1\\3&-5\end{bmatrix}=\begin{bmatrix}\text{x}&\text{x}^2\\3&-5\end{bmatrix} -5—(-3)=5\text{x}-3\text{x}^2 $
$-2=5\text{x}-3\text{x}^2$

$3\text{x}^2-5\text{x}-2=0$

Solving for x, we get

$\text{x}=2,-\frac{1}{3}$

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