math

posted by .

if x3+ax2-bx+10 is divisible by x2-3x+2 .find the value of a and b

• math -

since x^2 - 3x + 2 = (x-2)(x-1)
so x^3 + ax^2 -bx + 10 must be divisible by both
x-2 and x-1

let f(x) = x^3 + ax^2- bx + 10
f(2) = 5 + 4a - 2b + 10 = 0 ---> 4a - 2b = -15
f(1) = 1 + a - b + 10 ---> a-b = -11 or a = b-11

sub 2nd into 1st
4(b-11) - 2b = -15
4b - 44 - 2b = -15
2b = 29
b = 29/2
then a = 29/2 - 11 = 7/2

• math -

good

Similar Questions

1. math

I'm having some troubles with these. Thanks in advance. If a>0 find the minimum value. If a<0 find the maximum value. 1. y=-x²+2x+5 2. y=-2x²-3x+4 These are functions for parabolas, so f(x)=ax²+bx+c when a does not equal 0 …
2. Math

The question is this: You know that a number is divisible by 6 if it is divisible by both 3 and 2. So why isn't a number divisible by 8 if it is divisible by both 4 and 2?
3. math

is 504 divisible by 2,4,6,8 is 111 divisible by 3,9 is 3,217 divisible by 3 is 804 divisible by 2,4,6,8
4. math

find a such that f(x)= ax2-4x+3 has a maximum value of 12
5. math

find a such that f(x)= ax2-4x+3 has a maximum value of 12
6. math

Find the value of the missing digit that makes the statement true. 214,21_ is divisible by 11 Determine whether the statement is true or false. Why?