Question

If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2, find the values of a and b.​

Answer 1

Answer:

Step-by-step explanation:

Eq. is x³+ax²-bx+10 and have to check whether it is divisible by x²-3x+2?

First, solve this quadratic eq.  =x²-3x+2

by equating this, we have two roots (x)=2 and 1

Put these roots one by one on your eq. =x³+ax²-bx+10

put x=2 in eq.

8+4a-2b+10=0

4a-2b+18=0

4a-2b=-18...................................eq.(1)

put x=1, in eq

1+a-b+10=0

a-b+11=0

a-b=-11............................................eq.(2)

Now equate eq. (1)&(2)

4a-2b=-18

a-b=-11

{we have to make either a or b equal}

4a-2b=-18

2a-2b=-22  (this eq. multiplied with 2 so, that can cancel either a or b,and

                    here b will cancel)              

2a     =4

a=2

put this a in any eq. either in 1 or in 2

 b=13