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Manipal MET2011MathematicsQuadratic Equation

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

Options

  1. A(1,2)
  2. B(0,1)
  3. C(2,3)
  4. D(3,4)

Correct answer

B. (0,1)

Step-by-step solution

Let f(x)=a x^2+b x+c Again, let f(x)= f(x) d x= a 3 x^3+ b x^2 2 +c x At x=0 , f(0)=0 Agin, at x=1 aligned & f(1)= a 3 + b 2 +c & = 2 a+3 b+6 c 6 =0 aligned Hence, one root lies between (0,1) .

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