Question

if x3 +ax2 -bx +10 is divisible by x2 -3x +2,
find values of a and b

Answer 1

a=2, b=13

Step-by-step explanation:

let, given equation

x²-3x+2 = 0

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

x = 1,2

again

let, p(x) = x³+ax²-bx+10

A/Q,

p(x) is divisible by x²-3x+2

then,

p(1) = 0, and p(2) = 0

Now,

p(1) = 1³+a(1²)-b(1)+10=0

1+a-b+10=0

a-b=-11. (i)

again,

p(2) = 2³+a(2²)-b(2)+10=0

8+4a-2b+10=0

4a-2b=-18

2a-b=-9. (ii)

On solving both the equations,

a=2, and b=13