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Q.
If $x^{2}-3 x+2$ be one of the factors of the expression $x^{4}-p x^{2}+q$, then
Complex Numbers and Quadratic Equations
Solution:
Since $x^{2}-3 x+2$ is one of the factors of the expression $x^{4}-p x^{2}+q$,
therefore, on dividing the expression by factor, remainder $=0$
i.e., on dividing $x^{4}-p x^{2}+q$ by $x^{2}-3 x+2$, the remainder
$(15-3 p) x+(2 p+q-14)=0$
On comparing both sides, we get
$15-3 p=0 $
or $ p=5$
and $2 p+q-14=0$
or $q=4$.