First slide

Theory of equations

Question

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

Moderate

A

[3, 4]
B

[4, 5]
C

[4, 3]
D

[5, 4]

Solution

$x^{2} - 3 x + 2$ be factor of $x^{4} - {px}^{2} + q = 0$
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 $p - q - 1 = 0 . . (ii)$
Solving (i) and (ii), we get $[p, q] = [5, 4]$

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