Question

If $x^2-3x+2$ be one of the factors of the expression $x^4-p{x}^2+q$, then

• A. $p=4,q=5$
• B. $p=5,q=4$
• C. $p=-5,q=-4$
• D. None of these

Answer 1

Answer: (A)

Since $x^2-3x+2$ 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 $x^2-3x+2$, the remainder
$(15-3p)x+(2p+q-14)=0$
On comparing both sides, we get
$15-3p=0$
or $p=5$
and $2p+q-14=0$
or $q=4$.