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AP EAMCET202315 May 2023Evening ShiftMathematicsQuadratic EquationActual

If one root of the equation a x^3+b x+c=0 is twice another root, then

Options

  1. A36 b^3=343 a c^2
  2. B36 b^3+343 ac ^2=0
  3. C36 b^3+729 a c^2=0
  4. D36 b^3=729 ac^2

Correct answer

B. 36 b^3+343 ac ^2=0

Step-by-step solution

Let roots of equation be 2 , , So, 3 + =0 =-3 and 2 ^2 = -c a -6 ^3= -c a ^3= c 6 a Now, a ( c 6 a )+b ( c 6 a )^ 1 / 3 +c=0 aligned & b ( c 6 a )^ 1 / 3 = -c 6 -c & b^3 c 6 a = -343 c^3 36 6 36 b^3+343 c^2 a=0 aligned

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