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Manipal MET2020MathematicsQuadratic Equation

Roots of equation x^3-6 x+1=0 lie in the interval

Options

  1. A(2,3)
  2. B(3,4)
  3. C(3,5)
  4. D(4,6)

Correct answer

A. (2,3)

Step-by-step solution

Let f(x)=x^3-6 x+1 Now, f(2)=(2)^3-6 2+1=8-12+1=-3 and f(3)=(3)^3-6 3+1=27-18+1=10 Here, we see that f(2) and f(3) have opposite signs, so one of the roots lies in (2,3) .

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