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AP EAMCET202316 May 2023Evening ShiftMathematicsQuadratic EquationActual

If the equation 2 x^3+5 x^2-4 x-12=0 has a repeated root, then the constant term of the quadratic equation whose roots are the distinct roots of the given equation is

Options

  1. A-6
  2. B-5
  3. C-4
  4. D-2

Correct answer

A. -6

Step-by-step solution

Given equation 2 x^3+5 x^2-4 x-12=0 aligned & 2 x^3+4 x^2+x^2+2 x-6 x-12=0 & (2 x^2+x-6 )(x+2)=0 & (2 x^2+4 x-3 x-6 )(x+2)=0 aligned (2 x-3)(x+2)(x+2)=0 x=-2,-2, 3 2 so repeated roots =-2 , Now, quadratic equation aligned & x^2- (-2+ 3 2 ) x+(-2) 3 2 =0 & 2 x^2+x-6=0 Constant term =-6 aligned

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