Factor 8x^3+2x^2-20x-5
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Descartes' rule of signs tells you the one sign change in the coefficients means there's one positive real root. If you change the sign of the odd-power terms, the signs become -++-, so have two sign changes. This means there are 0 or 2 negative real roots.
A graph shows there to be 3 real roots, two of which are negative. Thus there are no complex roots.
A graph shows there to be 3 real roots, two of which are negative. Thus there are no complex roots.