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Question
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x4 - a2x2 + 3x - a.
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Solution
Let p(x) = x4 - a2x2 + 3x - a
Put x = -a in equation (i) we get
P(-a) = (-a)4 - a2 (-a)2 + 3(-a) -a
= a4 - a2 x a2 - 3a - a = -4a
But p(-a) = 0
⇒ -4a = 0
⇒ a = `(0)/(-4)`
⇒ a = 0.
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