If $|\begin{matrix} x - 4 & 2 x & 2 x \\ 2 x & x - 4 & 2 x \\ 2 x & 2 x & x - 4 \end{matrix}| = (A + B x) (x - A)^{2}$ , then the ordered pair (A,B) is equal to

(4,5)

(-4,-5)

(-4,3)

(-4,5)

Solution

(-4,5)

$∆ = |\begin{matrix} x - 4 & 2 x & 2 x \\ 2 x & x - 4 & 2 x \\ 2 x & 2 x & x - 4 \end{matrix}| x = - 4 m a k e s a l l t h r e e r o w i d e n t i c a l h e n c e, (x + 4)^{2} w i l l b e f a c t o r A l s o, C_{1} \to C_{2} + C_{2} + C_{2} ∆ = |\begin{matrix} 5 x - 4 & 2 x & 2 x \\ 5 x - 4 & x - 4 & 2 x \\ 5 x - 4 & 2 x & x - 4 \end{matrix}| \Rightarrow 5 x - 4 i s a f a c t o r ∆ = λ (5 x - 4) (x + 4)^{2} ∴ B = 5, A = - 4$

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Determinants

If $|\begin{matrix} x - 4 & 2 x & 2 x \\ 2 x & x - 4 & 2 x \\ 2 x & 2 x & x - 4 \end{matrix}| = (A + B x) (x - A)^{2}$ , then the ordered pair (A,B) is equal to

(4,5)

(-4,-5)

(-4,3)

(-4,5)

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Determinants

If x-42x2x2xx-42x2x2xx-4 = (A +Bx)(x-A)2, then the ordered pair (A,B) is equal to (4,5) (-4,-5) (-4,3) (-4,5)

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If $|\begin{matrix} x - 4 & 2 x & 2 x \\ 2 x & x - 4 & 2 x \\ 2 x & 2 x & x - 4 \end{matrix}| = (A + B x) (x - A)^{2}$ , then the ordered pair (A,B) is equal to

(4,5)

(-4,-5)

(-4,3)

(-4,5)