If $x^{2} + x - 1$ is factor of $x^{4} + p x^{3} + q x^{2} - 1,$ then the values of $p + q$ is:

3

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Solution

The correct option is B $3$
Let $x^{4} + p x^{3} + q x 2 - 1 = (x^{2} + x - 1) (x^{2} + t x + 1) . . . . . . . . . . . . . . . . . (1)$

Note that coeff. of $x^{2}$ and constant have been chosen to suit the product.

$x^{4} + p x^{3} + q x^{2} - 1 = x^{4} + (t + 1) x^{3} + t x^{2} + (t - 1) x - 1$

Comparing coefficients $t - 1 = 0 \Rightarrow t = 1$

$p = t + 1 = 2$

$q = t = 1$

Hence, $p + q = 1 + 2 = 3$

Suggest Corrections

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