Question

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

Answer 1

Answer:

Step-by-step explanation:

roots of x2+x-12 are -4,+3

so -4 and 3 are roots of p(x)

p(-4)=0

-64+16a-4b-84=0

16a-4b=148

4a-b=37      eqn1

p(3)=0

27+a9+b3-84=0

9a+3b=57

3a+b=19     eqn2

solving eqn1 and 2

we get

a=8,b=-5