Question

find all the zeros for f(x)=x^4-4x^3+x^2+8x-6

Answer 1

Found one!

Answer 2

(Try out the obvious numbers for some roots, then factorise the rest)

Note that if f(a) = 0, then (x-a) is a factor.

Answer 3

I found 3, is there more and how do I solve this?

Answer 4

f(3) = 0, yes.

So you can write f(x) (x-3)(ax^3 + bx^2 + cx +d)

And reduce it to a cubic. However there is one more (even easier!) factor you should be able to spot first. That will reduce it to a qudratic which you can formularise.

Answer 5

the number 1

Answer 6

Indeed.

=>

f(x) = (x-1)(x-3)(ax^2+bx+c)

Hint, once you find the last factor (quadratic) it will reduce no more so you'll need to use the formula or similar (or maybe common sense, once you see what it is).