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AP EAMCET202420 May 2024Morning ShiftMathematicsQuadratic EquationActual

If 2 x^2+3 x-2=0 and 3 x^2+a x-2=0 have one common root then the sum of all possible values of a is

Options

  1. A-3.5
  2. B7.5
  3. C-7.5
  4. D-1.5

Correct answer

B. 7.5

Step-by-step solution

2 x^2+3 x-2=0 x=-2, 1 2 If x=-2 is the common root with 3 x^2+a x-2=0 then 3(-2)^2+a(-2)-2=0 a=5 If x= 1 2 is the common root with 3 x^2+a x-2=0 then 3 ( 1 2 )^2+ a 2 -2=0 a=2.5 So, sum of all possible values of a=7.5

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