# Thread: Function Q help

1. ## 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.
Can anyone help me please?
Thanks

2. ## then 4f(0) = 5f(1) is

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.
Can anyone help me please?
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 $\displaystyle 5a + 5b + c + 5 = 0$

3. 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.

4. 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 ??

5. 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

6. eq#2 should of been 16a+4b+c = -64

your 7a-7b=91 should -7a-7b = 91 instead!

so then

[-7a - 7b = 91] x4 = -28a-56b = 224
[ 4a -8b = 32] x7 = 28a -28b = 364

-84b = 588
b = -7