Find the value of a & b, if $8 x^{4} + 14 x^{3} - 2 x^{2} + a x + b$ is divisible by $4 x^{2} + 3 x - 2$

(- 7, 7)

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(- 7, 2)

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(7, 2)

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None of these

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Solution

The correct option is B $(- 7, 2)$
$8 x^{4} + 14 x^{3} - 2 x^{2} + a x + b$ is divisible by $4 x^{2} + 3 x - 2$
$\Rightarrow$ remainder $= 0$
$({4 x}^{2} + 3 x - 2)) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ {8 x}^{4} + {14 x}^{3} - {2 x}^{2} a x + b {8 x}^{4} + {6 x}^{3} - {4 x}^{2}_________{8 x}^{3} + {2 x}^{2} - a x + b {8 x}^{3} + {6 x}^{2} - 4 x_{- 4 x}^{2} + (a + 4) x + b {- 4 x}^{2} - 3 x + 2___________0 + (a + 4 + 3) x + (b - 2)$
$(a + 7) x + (b - 2) = 0$
$\Rightarrow a + 7 = 0$ and $b - 2 = 0$
$\Rightarrow a = - 7$ and $b = 2$
$∴$ (a,b)=(-7,2)$

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