Question

If $x^2-3x+2$ be a factor of $x^4-p{x}^2+q$, then (p, q) =

• A. (3, 4)
• B. (4, 5)
• C. (4, 3)
• D. (5, 4)

Answer 1

The correct option is D

(5, 4)

$x^2-3x+2$ be factor of $x^4-p{x}^2+q=0$

Hence $(x^2-3x+2)=0$ ⇒ (x-2)(x-1) = 0

⇒ x = 2, 1, putting these values in given equation

so, 4p - q -16 = 0 ......(i)

and, p - q - 1 = 0 .......(ii)

Solving (i) and (ii), we get (p, q) = (5, 4)