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AP EAMCET202527 May 2025Morning ShiftMathematicsApplication of DerivativesActual

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least one root in (0,1) . Statement-II : Rolle's theorem is applicable to g ( x ) on [0,1] . Then

Options

  1. AStatement-I is false, Statement-II is true
  2. BStatement-I is true, Statement-II is false
  3. CStatement-I is true, Statement-II is true but Statement-II is not a correct explanation of Statement-I
  4. DStatement-I is true, Statement-II is true and Statement-II is a correct explanation of Statement-I

Correct answer

D. Statement-I is true, Statement-II is true and Statement-II is a correct explanation of Statement-I

Step-by-step solution

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