The remainder when $p (x) = 4 x - 5$ is divided by $x - 3$ is a zero of the polynomial $q (x) = 3 x^{2} + 5 x - a$ . What is the value of $a$ ?

182

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180

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114

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118

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Solution

The correct option is A 182
From remainder theorem,
the remainder when $p (x)$ is divided by $x - 3$ is $p (3)$ .

$∴$
$p (3)$ = $4 (3) - 5 = 12 - 5 = 7$

Given , 7 is a zero of the polynomial $q (x)$ .

$\Rightarrow$ $q (7) = 0$
$\Rightarrow$ $3 (7^{2}) + 5 (7) - a = 0$
$\Rightarrow$ $a = 182$

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