Consider the cubic equation

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider the cubic equation f(x)=x3−nx+1=0f(x)=x^3-nx+1=0, where n≥3n\geq3 and n∈Nn\in\mathbb{N}. Then f(x)=0f(x)=0 has (1) at least one root in (0,1)(0,1) (2) at least one root in (1,2)(1,2) (3) at least one root in (−1,0)(-1,0) (4) Data insufficient

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