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

MCQ

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
$(4, 3)$
✓
$(5, 4)$

✓

Answer

Correct option: D.

$(5, 4)$

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

Hence $({x^2} - 3x + 2) = 0\,\, \Rightarrow (x - 2)(x - 1) = 0$

==> $x = 2,\,1,$putting these values in given equation

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

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

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

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