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Question

If $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d$ is divisible by $a x to the power of 2 end exponent plus c$ , then $a comma blank b comma blank c comma d$ are in

A.P.
G.P.
H.P.
None of these

The correct answer is: None of these

Since $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d$ is divisible by $a x to the power of 2 end exponent plus c$ , therefore, when $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d$ is divided by $a x to the power of 2 end exponent plus c$ the remainder should be zero. Now when $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d$ is divided by $a x to the power of 2 end exponent plus c$ , then the remainder is $left parenthesis b c divided by a right parenthesis minus d$
$therefore blank fraction numerator b c over denominator a end fraction minus d equals 0$
$rightwards double arrow b c equals a d$
$rightwards double arrow fraction numerator b over denominator a end fraction equals fraction numerator d over denominator c end fraction$
Hence, from this, $a comma blank b comma c comma blank d$ are not necessarily in G.P.

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