If x=-1 is a root of the equation 2-x3334-x5354-x=0 then the other roots are

2-x3334-x5354-x=0 R2→R2-R3 2-x330-1-x1+x354-x=0 ⇒ 2-x63001+x39-x4-x=0 C2→C2+C3 ⇒ (1+x) (x-2) (x-9)-18=0 (x+1) x2-11x=0 x(x+1) (x-11)=0 x=0,-1,11

If x=-1 is a root of the equation 2-x3334-x5354-x=0 then the other roots are

2-x3334-x5354-x=0 R2→R2-R3 2-x330-1-x1+x354-x=0 ⇒ 2-x63001+x39-x4-x=0 C2→C2+C3 ⇒ (1+x) (x-2) (x-9)-18=0 (x+1) x2-11x=0 x(x+1) (x-11)=0 x=0,-1,11

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$If x = - 1 is a root of the equation |\begin{matrix} 2 - x & 3 & 3 \\ 3 & 4 - x & 5 \\ 3 & 5 & 4 - x \end{matrix}| = 0 then the other roots are$

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$0, 11 / 2$

0, 12

0, 11

11, 12

answer is C.

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Detailed Solution

$|\begin{matrix} 2 - x & 3 & 3 \\ 3 & 4 - x & 5 \\ 3 & 5 & 4 - x \end{matrix}| = 0 R_{2} \to R_{2} - R_{3} |\begin{matrix} 2 - x & 3 & 3 \\ 0 & - 1 - x & 1 + x \\ 3 & 5 & 4 - x \end{matrix}| = 0 \Rightarrow |\begin{matrix} 2 - x & 6 & 3 \\ 0 & 0 & 1 + x \\ 3 & 9 - x & 4 - x \end{matrix}| = 0 C_{2} \to C_{2} + C_{3} \Rightarrow (1 + x) [(x - 2) (x - 9) - 18] = 0 (x + 1) (x^{2} - 11 x) = 0 x (x + 1) (x - 11) = 0 x = 0, - 1, 11$