If x + a is a factor of x4 – a2 x2 + 3x – 6a. Find the value of a.
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Answer:
x+a is factor of x
4
−a
2
x
2
+3x−6a
Let p(x)=x
4
−a
2
x
2
+3x−6a
we know that if x−α is a factor of p(x) then p(α)=0
So p(−a)=0
(−a)
4
−a
2
(−a)
2
+3(−a)−a=0
a
4
−a
4
−3a−a=0
−4a=0
a=0
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