# Function Q help

• Dec 10th 2009, 12:47 PM
Detanon
Function Q help
f (x) = xcubed + axsquared + bx + c.
If f(-3) = 0, f (4) = 0 and 4f (0) = 5f (1)
find the values of the constants a , b and c.

I've made 2 linear simultaneous equations from the f -3 = 0 and f 4 = 0
but for the 4f 0 = 5f 1 I dont know what to do.
Thanks
• Dec 10th 2009, 01:08 PM
bigwave
then 4f(0) = 5f(1) is
Quote:

Originally Posted by Detanon
f (x) = xcubed + axsquared + bx + c.
If f(-3) = 0, f (4) = 0 and 4f (0) = 5f (1)
find the values of the constants a , b and c.

I've made 2 linear simultaneous equations from the f -3 = 0 and f 4 = 0
but for the 4f 0 = 5f 1 I dont know what to do.
Thanks

$\displaystyle 4f\left(0\right) = 4[(0)^3 + a(0)^2 + b(0) + c)] = 4c$

$\displaystyle 5f\left(1\right) = 5[(1)^3 + a(1)^2 +b(1) +c] = 5a +5b+5c + 5$

then $\displaystyle 4f(0) = 5f(1)$
is $\displaystyle 4c=5a +5b+5c + 5$
or $\displaystyle 5a + 5b + c + 5 = 0$
• Dec 12th 2009, 10:54 AM
Detanon
I cant get the question right, I keep getting it wrong..in my book it says the answer is a = -6, b =-7 , c =60
Can someone post the solution please?
Thanks.
• Dec 12th 2009, 12:49 PM
bigwave
Quote:

Originally Posted by Detanon
I cant get the question right, I keep getting it wrong..in my book it says the answer is a = -6, b =-7 , c =60
Can someone post the solution please?
Thanks.

if you plug these answers back into $\displaystyle f(-3)=0$, $\displaystyle f(4)=0$ and
$\displaystyle 5a + 5b + c + 5 = 0$

they do work so what is being done with the similtaneous equations is where the trouble is
its not an easy one to do

your similtaneous equation shoul look like this

9a-3b+c = 27
16a+4b+c = -64
5a+5b+c= -5

I put this into the SE on the TI89 and it returned your answers

still having ??
• Dec 12th 2009, 01:29 PM
Detanon
I keep getting b = 5???
from equation 1 and 2 I eliminate c. I get equation 4 which is 7a -7b = 91
from equation 1 and 3 i eliminate c. I get equation 5 which is 4a -8b = 32
• Dec 12th 2009, 01:46 PM
bigwave
eq#2 should of been 16a+4b+c = -64