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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:
x3 + ax2 - 2x + a + 4
Solution
Let p(x) = x3 + ax2 - 2x + a + 4 ...(i)
Since, (x + a) is a factor of p(x), so p(-a) = 0
Put x = -a in equation (i), we get
p(-a) = (-a)3 + a(-a)2 -2(-a) + a + 4
= -a3 + a(a2) + 2a + a + 4
= -a3 + a3 + 3a + 4
= 3a + 4
But p(-a) = 0
⇒ 3a + 4 = 0
⇒ 3a = -4
⇒ a =
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