Question

use descartes rule of signs to find how many possible positive real roots this polynomial has:
$p(x)=4x^{5}-9x^{4}-x^{3}+8x^{2}+x$
3 or 1
1
2 or 0

Explanation:

Step1: List polynomial sign sequence

$+4x^5, -9x^4, -x^3, +8x^2, +x$ → Signs: $+, -, -, +, +$

Step2: Count sign changes

Change 1: $+$ to $-$; Change 2: $-$ to $+$ → Total 2 changes.

Step3: Apply Descartes Rule

Subtract even integers from total changes: $2$ or $2-2=0$.

Answer:

2 or 0