Use Descartess Rule of Signs to analyze the nature of the ro

Use Descartes\'s Rule of Signs to analyze the nature of the roots of 3x^4 - 2x^3 + 6x^2 + 5x - 2 = 0

Solution

f(x) = 3x^4 - 2x^3 + 6x^2 +5x -2

sign changes in f(x) = 3

max number of +ve roots = 3

This means that there are 3 or 1 positive real roots.

Lets check f(-x) = 3(-x)^4 - 2(-x)^3 +6(-x)^2 + 5(-x) -2

= 3x^4 +2x^3 +6x^2 - 5x -2

No. of sign changes = 1

So, there are 3 or 1 positive roots and 1 -ve root