Question

Locate the situation of the roots of the equation givem below :x^3+x^2-2x-1=0

Answer 1

Given equation is x³ + x² - 2x - 1 = 0

Since only one time sign changes from going left side to right side.

So, only one real root is possible.

\(\because\) f(0) = -1 & f(-1) = -1 + 1 + 2 - 1 = 1 > 0, where f(x) = x³ + x² - 2x - 1

\(\therefore\) f(0) f(-1) < 0

\(\therefore\) Root lies between 0 and -1.