Question

Which describes the number and type of roots of the equation x^3 - 4x^2 + 50x + 7 = 0?

a. 1 positive, 2 negative
b. 2 positive, 1 negative
c. 3 negative
d. 3 positive

I know I asked this before but I'm going over it and I don't understand it. I got help from someone and they said the answer was b, but I still don't understand it.

Answer 1

(x-a)(x-b)(x-c) = 0
well -a * -b * - c = +7
they can not all be + or no +7 OUT
so they could all be - but then I would not get -4 anywhere OUT
if a is - and 2 others + that would get +7 YES
if a is + and two others - that gets for -7 OUT

Answer 2

Using Descartes' Rule of Signs,
f(x) has 2 sign changes. so, 2+ or 0+
f(-x) has 1 sign change, so 1-

Looks like 2+, 1-

0+ and 1- is also a possibility, but not one of the choices...