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). 

Answer 1

(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