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Manipal MET2016MathematicsQuadratic Equation

If 2 a+3 b+6 c=0 , then atleast one root of the equation a x^2+b x+c=0 lies in the interval

Options

  1. A(0,1)
  2. B(1,2)
  3. C(2,3)
  4. DNone of these

Correct answer

A. (0,1)

Step-by-step solution

Consider the function f(x)= a x^3 3 + b x^2 2 +c x+d We have, f(0)=d and f(1)= a 3 + b 2 +c+d aligned & = 2 a+3 b+6 c 6 +d & = 0 6 +d [ 2 a+3 b+6 c=0] aligned Therefore, 0 and 1 are roots of the polynomial f(x) . Hence, according to Rolle's theorem, there exists atleast one root of the polynomial f^ (x)=a x^2+b x+c lying between 0 and 1.

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