# Zeros of a function

• Apr 19th 2012, 10:58 PM
iFuuZe
Zeros of a function
3. Find all rational zeros of the function:

f(x)=25x^4+25x^3-154x^2-4x+24

got no ide how to do it.

4. Given that (1-i) is a zero of the function:

f(x)=4x^4-11x^3+14x^2-6x

Find all the zeros of the function.

Now for question 4 i got [x-(1-i)], [x-(1-i)] as conjugates now i factor them which gives x^2-2x+2, and now when i use long division ikeep getting -12x^2 as a remainder??????
• Apr 19th 2012, 11:39 PM
a tutor
Re: Zeros of a function
To get started you could evaluate f(x) with x= some factor of 24.

Once you have one or two roots you could then use polynomial division.
• Apr 19th 2012, 11:42 PM
iFuuZe
Re: Zeros of a function
i dont understand what you mean mate
• Apr 19th 2012, 11:52 PM
biffboy
Re: Zeros of a function
Need to 'guess one solution' so we will have our 1st factor and can divide to find other factors. If ax-b is 1st factor a must be factor of 5 and b factor of 24.
• Apr 20th 2012, 12:28 AM
a tutor
Re: Zeros of a function
For your second question, you're right to be dividing by x^2-2x+2. It's your division that's going wrong. You should get 4x^2-3x and no remainder.
• Apr 20th 2012, 03:03 AM
iFuuZe
Re: Zeros of a function
yep youre right now im not sure how i would go about factorising 4x^2-3x