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Question
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x5 - 3x4 - ax3 + 3ax2 + 2ax + 4.
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Solution
Let p(x) = x5 - 3x4 - ax3 + 3ax2 + 2ax + 4 ...(i)
Since, (x - 2) is facxtor of p(x), so p(2) = 0
Put x = 2 in equation (i) we get
p(2) = (2)5 - 3(2)4 -a(2)3 + 3a(2)2 + 2a(2) + 4
= 32 - 3 x 16 - a x 8 + 3a x 4 + 4a + 4
= 32 - 48 - 8a + 12a + 4a + 4
= 8a - 12
But p(2) = 0
⇒ 8a = 12 = 0
⇒ a = `(12)/(8)`
⇒ a = `(3)/(2)`.
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