Question

question 1 of 10
which of the following expresses the possible number of positive real
solutions for the polynomial equation shown below?
\\(5x^3 + x^2 - 7x + 28 = 0\\)

\\(\bigcirc\\) a. three or one
\\(\bigcirc\\) b. zero
\\(\bigcirc\\) c. one
\\(\bigcirc\\) d. two or zero

Explanation:

Step1: Apply Descartes' Rule of Signs

Count sign changes in \(5x^3 + x^2 - 7x + 28\):
+ to -, - to + → 2 sign changes.

Step2: Determine possible positive roots

Number of positive real roots = number of sign changes or less by even integer: 2 or 0.

Answer:

D. Two or zero