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AP EAMCET202125 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

The solution of the equation 2 x^3-x^2-22 x-24=0 , when two of the roots are in the ratio 3: 4 is

Options

  1. A3,4, 1 2
  2. B-3 2 ,-2,4
  3. C-1 2 , 3 2 , 2
  4. D-3 2 , 2, 5 2

Correct answer

B. -3 2 ,-2,4

Step-by-step solution

Given equation, 2 x^3-x^2-22 x-24=0 Put x=-2 aligned & 2(-2)^3-(-2)^2-22(-2)-24 & -16-4+44-24=0 aligned x+2 is root of equation 2 x^3-x^2-22 x-24=0 aligned & 2 x^3-x^2-22 x-24=(x+2) (2 x^2-5 x-12 ) & =(x+2) (2 x^2-8 x+3 x-12 ) & =(x+2)(2 x+3)(x-4) aligned Roots of equation are -2, -3 2 , 4

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