Engineering
Mathematics
Quadratic Equation and Nature of Roots
Question
If x2 – 3x + 2 be a factor of x4 – px2 + q, then p + q is equal to
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Solution
x2 – 3x + 2 = (x – 1) (x – 2) is a factor of x4 – px2 + q
x = 1 and 2 are roots
1 – p + q = 0 ⇒ p – q = 1 ……(i)
and 16 – 4p + q = 0 ⇒ 4p – q = 16 ……(ii)
From (ii) – (i)
3p = 15
⇒ p = 5
q = 4
p + q = 9