If $x - 2$ and $x - 1$ are the only zeroes of the polynomial $p (x)$ , which of the following is a zero of the polynomial $p (x) - 6$ ?

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-4

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Solution

The correct option is C 4
$∵$ $x - 2$ and $x - 1$ are the only factors of $p (x)$

$\Rightarrow$ $p (x) = (x - 1) (x - 2)$
$\Rightarrow$ $p (x) = x^{2} - 2 x - x + 2$
$\Rightarrow$ $p (x) = x^{2} - 3 x + 2$

$∴$ $p (x) - 6$
$\Rightarrow$ $x^{2} - 3 x + 2 - 6$
$\Rightarrow$ $x^{2} - 3 x - 4$

Let $q (x) = x^{2} - 3 x - 4$

From the options, we have 4 is a zero as q(x)
$∵$ $\Rightarrow$ $4^{2} - 3 (4) - 4 = 0$

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