how do you do this???---Find how many possible complex roots there are for this function.

Question

how do you do this???--->Find how many possible complex roots there are for this function.

anonymous · Answer

$$H(x)=4x ^{4}-5x ^{3}+2x ^{2}-x+5$$

nory · Answer

The equation is of the fourth degree, so we know that there are at most four solutions. Yes?

anonymous · Answer

yes

nory · Answer

Now if the equation were odd degree, we would have a little more trouble, because we know that there must be an even number of complex roots. (Because they come in pairs.) But it is of even degree.
Now just use Descartes' method. Do you know that one, with the adding and subtracting?

anonymous · Answer

can you give me a refresher

nory · Answer

To count how many positive real roots there are, you look at the coefficients and count how many times they change sign (from positive to negative or vice versa).
Watch:
|dw:1379045847856:dw|
It changes signs four times, and so there are four real roots.
What does that say about the problem you wanted to solve?