Question

If p(x) x cube + k x square + hx + 6 and x+1 and x-2 are factors of P(x), then find the values of H and K.

Answer 1

Answer:

p(x)=x^3+kx^2+hx+6

g(x)=x+1

x=-1

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

=-1-k-h+6

=-k-h=-5

=-(k+h)=-5

=k+h=5 (1)

g(x)=x-2

x=2

(2)^3+k(2)^2+h(2)+6

=8+4k+2h+6

=14+4k+2h

=4k+2h=-14

=2(2k+h)=-14

=2k+h=-7 (2)

=Subtracting both equation

=k+h=5

2k+h=-7

- - +

----------------

-2k=12

k=-6

puttin g value in eq.

-6+h=5

=h=5+6

=h=11

k=-6,h=11