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Absolute Value Function

If x+1 is a...

Question

If $(x + 1)$ is a factor of $x^{4} + (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 9) x + 6$ , then the value of $p$ is:

- 4

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0

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4

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2

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Solution

The correct option is C $4$
$x + 1$ is a factor $\Rightarrow x = - 1$ is a root of given equation.
Substituting $x = - 1$ in the given equation, we get
$(- 1) + (p - 3) (- 1) - (3 p - 5) (1) + (2 p - 9) (- 1) + 6 = 0$
$1 - p + 3 - 3 p + 5 - 2 p + 9 + 6 = 0$
$- 6 p + 24 = 0$
$\Rightarrow p = 4$

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