Question

If x2+x-12 divides f x=x3+ax2+bx-84 exactly find a and b

Answer 1

See the attachment for detail solution
Hope it will help you

Answer 2

Answer:

a=8 and b=-5

Step-by-step explanation:

Given: The equation $x^2+x-12$ divides the equation $x^3+ax^2+bx-84$exactly.

To find: The value of a and b.

Solution: Since, The equation $x^2+x-12$ divides the equation $x^3+ax^2+bx-84$exactly, thus we have the remainder equals to 0.

Now, on dividing the given equation by  $x^2+x-12$, we get

$(a-8)x^2+(b+5)x=0$

On comparing the above equation with the given equation $f(x)=x^3+ax^2+bx-84$, we get

a=8 and b=-5