If $$f(x)=a$$−$$10axa$$−$$1ax2axa$$, then $$f(2x)$$−$$f(x)$$ is divisible by

Correct option is 1,2,3undefined

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If $f (x) = |\begin{array}{ccc} a & - 1 & 0 \\ ax & a & - 1 \\ {ax}^{2} & ax & a \end{array}|$ , then $f (2 x) - f (x)$ is divisible by

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detailed solution

Correct option is A

Applying R3→R3−xR2 and R2→R2−xR1, we getf(x)=a−100a+x−100a+x=a(a+x)2Hence,f(2x)−f(x)=a(a+2x)2−(a+x)2=a(a+2x−a−x)(a+2x+a+x)=ax(2a+3x)

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If f(x)=a−10axa−1ax2axa, then f(2x)−f(x) is divisible by

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If $f (x) = |\begin{array}{ccc} a & - 1 & 0 \\ ax & a & - 1 \\ {ax}^{2} & ax & a \end{array}|$ , then $f (2 x) - f (x)$ is divisible by