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

(3,4)

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(4,5)

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(4,3)

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(5,4)

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Solution

The correct option is D (5,4)
$x^{2} - 3 x + 2$ be factor of $x^{4} - p x^{2} + q = 0$
Hence $(x^{2} - 3 x + 2) = 0 \Rightarrow (x - 2) (x - 1) = 0 \Rightarrow x = 2, 1,$ putting these values in given equation
So $4 p - q - 16 = 0 . . . . . . . . (i)$
And $p - q - 1 = 0 . . . . . . . (i i)$
Solving (i) and (ii), we get $(p, q) = (5, 4)$

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