Question

use descartes rule of signs to find how many possible positive real roots this polynomial has:
$p(x) = 5x^5 - 8x^4 + 3x^3 - 7x^2 + 2x$
1
4, 2 or 0
0

Explanation:

Step1: List polynomial coefficients

$+5, -8, +3, -7, +2, 0$

Step2: Count sign changes

Sign changes: $+5\to-8$, $-8\to+3$, $+3\to-7$, $-7\to+2$ (4 total)

Step3: Apply Descartes Rule

Subtract even integers from 4: $4, 4-2=2, 2-2=0$

Answer:

4, 2 or 0