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Q.

If ${ax}^{3} + 3 x^{2} - 13$ and $2 x^{3} - 5 x + a$ are divided by $(x - 2)$ leave the same remainder, then a =

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a

0

b

2

c

1

d

4

answer is C.

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Detailed Solution

$f (2) = a {(2)}^{3} + 3 {(2)}^{2} - 13$
$\begin{array}{l} = 8 a + 12 - 13 \\ = 8 a - 1 \\ s (2) = 2 (2)^{3} - 5 (2) + a \\ = 16 - 10 + a \\ = 6 + a \end{array}$
Same remainder
$\begin{array}{l} f (2) = g (2) \\ 8 a - 1 = 6 + a \\ 8 a - a = 6 + 1 \\ 7 a = 7 \\ a = \frac{7}{7} \\ a = 1 \end{array}$

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