First slide

Sequence and Series

Question

If ${ax}^{3} + {bx}^{2} + cx + d$ is divisible by ${ax}^{2} + c$ ,then a, b, c, d are in

Moderate

A

AP
B

GP
C

HP
D

None of these

Solution

Since, ${ax}^{3} + {bx}^{2} + cx + d$ is divisible by ${ax}^{2} + c$ .
Therefore, when ${ax}^{3} + {bx}^{2} + cx + d$ is divided by al + c, the remainder is zero
$\begin{array}{l} ∴ d - \frac{bc}{a} = 0 \\ \Rightarrow bc = ad \Rightarrow \frac{b}{a} = \frac{d}{c} \\ \Rightarrow a, b, c, d are in GP. \end{array}$

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