Descartes' Rule of Signs
f(x)=3x^4-11x^3+10x-4

I don't really understand Descartes' rule of signs, but I've come up with the possibilities of:
3 Positive, 1 Negative, 0 Complex.
1 Positive, 1 Negative, 2 Complex.

Can anyone verify if this is correct/if I've done it correctly?

Question

Descartes' Rule of Signs
f(x)=3x^4-11x^3+10x-4

I don't really understand Descartes' rule of signs, but I've come up with the possibilities of:
3 Positive, 1 Negative, 0 Complex.
1 Positive, 1 Negative, 2 Complex.

Can anyone verify if this is correct/if I've done it correctly?

anonymous · Answer

the positive zeros are how many sign changes there are and the negatives are if you plug (-x) into x how many sign changes you have. and since you can only have 4 zeros at most and there are 3 sign changes you know there cant be any complex since there has to be a conjugate with any nonreal zero