Question

Find a and b such that (x+1) and (x+2) are factors of p(x) =x^3+ax^2-bx+10

Answer 1

Answer:

Step-by-step explanation:

Since x+1 and x+2 are the factors

So, x= -1 and x=-2

Putting the value in the given equation

That is x^3 +ax^2-bx+10

X=-1

(-1)'3+a(-1)^2-b(-1)+10=0

-1+a+b+10...........1

X=-2

(-2)^3++a(-2)^2-b(-2) +10=0

-8+4a+2b+10.......2

Multiplying 1equation by 2

2(-1+a+b+10

-2+2a+2b+20 ..,...3

Subtracting 3 from 2

-8+4a+2b+10

+2-2a-2b-20

=-6+2a-10=0

2a=16

A=8

Putting the value of a in any of equation

That is -1+a+b+10 =0

-1+8+b+10=zero

Transposing 17 to another side

That ll b =-17