Question

use descartes rule of signs to find how many possible positive real roots this polynomial has:
$p(x) = -7x^4 + 3x^3 - 9x^2 + x + 6$
1
3 or 1
2 or 0

Explanation:

Step1: List polynomial sign sequence

Signs of $P(x) = -7x^4 + 3x^3 - 9x^2 + x + 6$: $-, +, -, +, +$

Step2: Count sign changes

Count sign transitions: $-\to+$, $+\to-$, $-\to+$ → 3 changes.

Step3: Apply Descartes Rule

Subtract even integers from 3: $3-2=1$.

Answer:

3 or 1