If $x^{2} + x - 1$ is a factor of $x^{4} + p x^{3} + q x^{2} - 1$ then the values of p and q can be -

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Solution

$\Rightarrow 2 p - q - 3 = 0, p - q - 3 = 0$
$\Rightarrow 2 p - q = 3, p - q = 3$
$\Rightarrow 2 p - q - p + q = 3 - 3$ by soving $2 p - q = 3, p - q = 3$
$\Rightarrow p = 0$
$\Rightarrow q = p - 3 = 0 - 3 = - 3$ using $p - q = 3$
$∴ p = 0, q = - 3$

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