Find x, so that 1 x 1 132051032 11x =0 - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$\frac{- 9 \pm \sqrt{53}}{4}$
B
$\frac{- 5 \pm \sqrt{53}}{2}$
C
$\frac{- 9 \pm \sqrt{53}}{2}$
D
$\frac{7 \pm \sqrt{53}}{2}$

Solution:

We have, $[1 x 1] [\begin{matrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ x \end{matrix}] = 0$

$\Rightarrow [\begin{matrix} 1 & 5 x + 6 & x + 4 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ x \end{matrix}] = 0 \Rightarrow [\begin{matrix} 1 + 5 x + 6 + x^{2} + 4 x \end{matrix}] = 0$

$\Rightarrow$ $x^{2} + 9 x + 7 = 0$

$∴ x = \frac{- 9 \pm \sqrt{81 - 28}}{2} \Rightarrow x = \frac{- 9 \pm \sqrt{53}}{2}$

Find $x,$ so that $[1 x 1] [\begin{matrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ x \end{matrix}] = 0$

Solution:

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