If a polynomial $p (x) = x^{2} - a x + b$ has two zeroes 1 and 7, then the value of $a b$ is .

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Solution

The correct option is C 56
$∵$ 1 is a zero,
$p (1) = 0$
$\Rightarrow$ $1^{2} - a + b = 0$
$\Rightarrow$ $a - b = 1$ ......eq (i)

Also,
$∵$ 7 is also a zero,
$p (7) = 0$
$\Rightarrow$ $7^{2} - (7) a + b = 0$
$\Rightarrow$ $7 a - b = 49$ ......eq (ii)

Subtracting (i) from (ii), we have
$7 a - b - a + b = 48$
$\Rightarrow$ $6 a = 48$
$\Rightarrow$ $a = 8$

Substituting $a = 8$ in eq (i), we have
$8 - b = 1$
$\Rightarrow$ $b = 7$

$∴$ $a b = (8) (7) = 56$

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