Honours Maths Help!!

natrisioga

Hi,

Just wondering if someone could help me solve this question, or at least point me in the right direction.

f(x) is a cubic polynomial
f(-1)=0
f(1)=0
f(2)=5f(0)

Find the equation f(x). Now find 3 roots of f(x)=0

Thanks

Jonathan

natrisioga wrote: »

Hi,

Just wondering if someone could help me solve this question, or at least point me in the right direction.

f(x) is a cubic polynomial
f(-1)=0
f(1)=0
f(2)=f(0)

Find the equation f(x). Now find 3 roots of f(x)=0

Thanks

Ok so let

f(x) = ax^3 + bx^2 + cx + d

f(-1) = a + b - c + d = 0

f(1) = a + b + c + d = 0

f(2) = f(0) = d

That should put you in the right direction.

Since f(x) is a cubic polynomial, it means f(x) = ax^3+bx^2+cx + d. Since f(-1) = 0, you get..

-a + b - c + d = 0

And then with f(1) = 0, you get...

a + b + c + d = 0

and for f(2) = 0, you get...

8a + 4b + 2c + d, which is the same as f(0) which is 0+0+0+d, and so you get 8a + 4b + 2c = 0. Do some simultaneous equations, and you find you a and b and c and d.

Once you have the equation you can divide in, although you're already given that f(-1) = f(1) = 0, so you only have to find one more root.

Jonathan

lol sorry bout that... made a mess of that.. Meant to sub the values in to the x's not the coeffients

natrisioga

Sorry, just realised now I made an error

Its f(2) = 5f(0)

Thanks for the help