Question

Find the value of a and b if x3+10x2+ax+b is exactly divisible by x-1 and x-2

Answer 1

Hey.

Here is the answer.

As x^3+10x^2+ax+b is exactly divisible by
x-1 and x-2
So, x-1 =0 and x-2= 0 are two factors of the expression.
So, 1 and 2 are two zeros of the expression .

So, by putting x=1 in the expression
1^3+10×1^2+a×1+b=0
or, 1+10+a+b=0
or, a+b+11=0________________1st

Also, by putting x=2,
2^3+10×2^2+a×2+b=0
or, 8+40+2a+b=0
or, 2a+b+48=0______________2nd

Substracting 1st from 2nd, we get
a+37=0
so, a= - 37

b= -a -11 {from 1st}
so, b=-(-37)-11=37-11 =26

Hence , a= -37 & b = 26.

Thanks.