Question

Find the value of 'p' and 'q' if x-1 and x-2 are factors of 2x^3 + px^2+ qx -14

Answer 1

Let f(x) = 2x^3 + px^2+ qx -14

if x-1 is a factor of f(x) then f(1) =0
putting x=1

f(1) = 2(1)^3 + p(1)^2 + q*1 -14 = 0
⇒ 2+p+q-14 = 0
⇒ p+q = 12 ...........1)

similarly if x-2 is a factor of f(x), then f(2) = 0
putting x=2

f(2) = 2(2)^3 + p(2)^2 + q*2 -14 = 0
⇒ 16 + 4p + 2q-14 = 0
⇒ 2(2p +q) = 2
⇒ 2p+q = 1 .............2)

from 1) and 2) we have
p+ p + q=1
p+12 = 1
p= -11

q = 12-p = 12+11 = 23

Ans. p= -11. q=23