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Question
Find the values of p and q in the polynomial f(x)= x3 - px2 + 14x -q, if it is exactly divisible by (x-1) and (x-2).
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Solution
(x - 1) ⇒ x = l .... (i)
(x - 2) ⇒ x = 2 .... (ii)
Putting (i) in polynomial , we get
f(l) = 1× 1 × 1 - p × 1 × 1 + 14 × 1 - q = 0
⇒ p + q = 15
⇒ p = 15 - q
Putting (ii) in polynomial , we get
f(2) = 2 × 2 × 2 - p × 2 × 2 + 14 × 2 - q = 0
4p + q= 36, ⇒ q = 36 - 4p .... (iv)
Combining (iii) and (iv), we get,
p = 15 - (36 - 4p)
⇒ p= 15 - 36 + 4p
⇒ 3p = 21
q = 36 - 4 × 7 = 8
⇒ p = 7 , q = 8
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