Question
If x2 - 3x + 2 is a factor of, x4
- px2 + q, then (p, q) =Solution
The factors of x2 - 3x + 2 are (x - 1) and (x - 2)  Let f(x) = x4 - px2 + q Since, f(x) is divisible by (x - 1) and (x - 2) f(1) = 0 and f(2) = 0 f(1) = 14 - p(1)2 + q = 0 f(1) = 1 - p + q = 0 …..(1) f(2) = 24 - p(2)2 + q = 0 f(2) = 16 - 4p + q = 0 ------ ( 2 ) Solving (1) and (2), we get p = 5; q = 4
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