of each equation using Descartes Rule o ) 2x^3-3x^2+5x-6=0

To determine the possible number of positive and negative real roots of the equation using Descartes' Rule of Signs, we need to analyze the signs of the coefficients.### Positive Real RootsDescartes' Rule of Signs states that the number of positive real roots of a polynomial is equal to the number of sign changes between consecutive non-zero coefficients, or less than that by an even number.For the polynomial :- The coefficients are: - The signs of the coefficients are: Count the number of sign changes:- From to : 1 change- From to : 1 change- From to : 1 changeThere are 3 sign changes, so the possible number of positive real roots is 3, 1 (3 minus an even number).### Negative Real RootsTo find the possible number of negative real roots, we substitute with and then apply the same rule.Substitute with : The coefficients are: The signs of the coefficients are: Count the number of sign changes:- There are no sign changes.Since there are no sign changes, there are 0 negative real roots.### Summary- Possible number of positive real roots: 3 or 1- Possible number of negative real roots: 0Thus, the equation can have either 3 or 1 positive real roots and no negative real roots.