If $(x^{2} - 3 x + 2)$ is a factor of $x^{4} - {p x}^{2} + q$ , then p and q are respectively ............
find the sum of p and q.

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Solution

Given $x^{2} - 3 x + 2$ is a factor of $x^{4} - p x^{2} + q$
$\Rightarrow (x - 1)$ and $(x - 2)$ are factors of $x^{4} - p x^{2} + q$
So, $x = 1, 2$ satisfies $x^{4} - p x^{2} + q$
$\Rightarrow 1 - p + q = 0$
and $16 - 4 p + q = 0$
Solving these eqns , we get
$p = 5, q = 4$
$\Rightarrow p + q = 9$

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If (x2−3x+2) is a factor of x4−px2+q, then p and q are respectively ............find the sum of p and q.

Given x2−3x+2 is a factor of x4−px2+q⇒(x−1) and (x−2) are factors of x4−px2+qSo, x=1,2 satisfies x4−px2+q⇒1−p+q=0and 16−4p+q=0Solving these eqns , we get p=5,q=4⇒p+q=9

If $(x^{2} - 3 x + 2)$ is a factor of $x^{4} - {p x}^{2} + q$ , then p and q are respectively ............
find the sum of p and q.

Given $x^{2} - 3 x + 2$ is a factor of $x^{4} - p x^{2} + q$
$\Rightarrow (x - 1)$ and $(x - 2)$ are factors of $x^{4} - p x^{2} + q$
So, $x = 1, 2$ satisfies $x^{4} - p x^{2} + q$
$\Rightarrow 1 - p + q = 0$
and $16 - 4 p + q = 0$
Solving these eqns , we get
$p = 5, q = 4$
$\Rightarrow p + q = 9$