Question

If P(x)=x^3+kx^2+hx+6 and x+1 and x-2 are the factors of p(x) then find the values of h and k

Answer 1

Hey.

Here is the answer.

As, x+1 and x-2 are factors
so, -1 and 2 are zeros

So,

p(-1) = (-1)^3 +k(-1)^2 +h(-1) +6 = 0

or, 0 = -1 + k - h +6

or, k - h = - 5...........(1)

Also, p(2)= 2^3+k(2)^2+h(2)+6 = 0

or, 8 + 4k + 2h + 6 = 0

or, 2k + h = - 7.........(2)


Adding (1) & (2),

3k = - 12

so, k = - 4

so, h = k + 5 = -4 + 5

or, h = 1

Thanks.