Question

If x square 3+ ax square 2-bx+10 is divisible by x square 2-3x+2, find the values of a and b.​

Answer 1

factorising x²-3x+2

x²-2x-x+2=0

x(x-2)-1(x-2)=0

(x-1)(x-2)=0

factors of x²-3x+2 are (x-2)(x-1)

hence,f(1)=0

(1)³+a(1)²-b(1)+10=0

1+a-b+10=0

a-b= -11-------------(1)

f(2)=0

(2)³+a(2)²-b(2)+10=0

8+4a-2b+10=0

4a-2b= -18

2a-b= -9------------(2)

subtracting (1) from (2)

2a-b-(a-b)= -9-(-11)

2a-b-a+b= -9+11

a=2

now putting the value of a in (1)

a-b= -11

2-b= -11

-b= -11-2

-b= -13

b=13

a=2 and b=13