• anonymous
I was trying to find the roots of the polynomial f(x) = 4x^3+3x^2-6x-1. By Rolle's theorem, If there exists 2 different values of x, say x(1) and x(2) that returns a same value of f(x), then at some point between x(1) and x(2), d/dx[f(x)] = 0. ---> (1) Hence, I differentiate f(x) to get, d/dx[f(x)] = 12x^2+6x-6 By (1) 12x^2+6x-6 = 0 Solving for x, i get 2 roots, x = -1 and 1/2. Now solve for f(x) = 4x^3+3x^2-6x-1 with x = 1 (by changing the sign) and surprisingly, f(1) = 0 !!, seems to be one of the root of f(x). Can someone help me to understand this ?
OCW Scholar - Single Variable Calculus
• Stacey Warren - Expert brainly.com
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