Question

find the value of p+q if the hcf of the polynomials x³-3x²+px+24 and x²-7x+q is (x-2)​

Answer 1

x-2 = 0 as it is the hcf of both polynomials

x = 2

then,

p(x) = x3 -3x^2 +px +24 = 0

p(2) = (2)^3- 3(2)^2 +p*2 +24 = 0

8-12+2p +24 = 0

20+2p = 0

2p = -20

p = -10

then,

p(x) = x^2 -7x +q = 0

p(2) = (2)^2 -7*2 +q = 0

4 -14 +q = 0

-10 +q = 0

q = 10

then, p+q

-10 +10 = 0

so the answer is 0