- #1
Clever Penguin
- 74
- 20
Homework Statement
[/B]
f(x) = 2x3+ax2+bx+10
When f(x)/(2x-1) the remainder is 12
When f(x)/(x+1) there is no remainder
a) Find the value of a and b
b) Show that f(x) = 0 has only one root
Homework Equations
None
The Attempt at a Solution
a) (2x-1)=0x=1/2
f(1/2) = 12 = 2(1/2)3+b(1/2)2+a(1/2)+10
1/4+a/4+b/2+10=12
1+a+2b+40=48
a+2b=7
(x+1)=0
x=-1
f(-1)= 0 = 2(-1)3+a(-1)2+b(-1)+10
a-b+8=0
b=a+8
b=(7-2b)+8
b=15-2b
3b=15
b=5
a=7-2b
a=7-10
a=-3
a=-3 and b=5
b) 2x3-3x2+5x+10=0
Now I need to factorise this, but I don't know how
I tried using x as a common factor, but its not. 10 does not have a factor of x.
Last edited: