Algebra Descartes rule

Question

Use​ Descartes's rule of signs to discuss the possibilities for the roots of the equation. Do not solve the equation.

x^3+7x^2+2x+4=0

A 1 Positive real root and 2 negative real roots

B 1 Negative real root and 2 imaginary roots

C 1 Positive real root and 2 imaginary roots

D 3 Positive real root

E 1 Negative real root and 2 positive real root

F 3 Negative real roots

Answer 1

x^3 +7x^2 +2x + 4 = 0

no sign changes, then no positive real roots

substitute -x for x to get

-x^3 +7x^2 -2x +4 = 0

3 sign changes, so either 1 or 3 negative real roots and 0 or 2 imaginary roots

(zero is not a root, as 4 doesn't = 0)

A and C through E not possible

only F & B are possible: 3 negative real roots