Question

if and b are the number of positive and negative roots of the equation ||x-1|+|x+1|-2|x-2||=sin x then the value of b+1/a is​

Answer 1

Use Descartes' Rule of Signs to determine the number of real zeroes of:

f (x) = x5 – x4 + 3x3 + 9x2 – x + 5

Descartes' Rule of Signs will not tell me where the polynomial's zeroes are (I'll need to use the Rational Roots Test and synthetic division, or draw a graph, to actually find the roots), but the Rule will tell me how many roots I can expect, and of which type.