Question

how many negative roots does 5x^4-7x^3-x^2-3x-2

Answer 1

One. Refer to the attached plot.

Answer 2

Formula: http://en.wikipedia.org/wiki/Quartic_function

Answer 3

Let \(\large 5x^4-7x^3-x^2-3x-2\\
\Large =(x^2 +px+q)(x^2+rx+s)\\
\Large =x^4+(p+r)x^3+(q+s+pr)x^2+(ps+qr)x+qs\)
By equating coefficients, this results in the following set of simultaneous equations:
\(\Large 5=p+r\\ \Large -7=q+s+pr\\ \Large -1=ps+qr\\ \Large -2=qs\)
Now you just need calculation to find p, q, r, s