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AP EAMCET202423 May 2024Morning ShiftMathematicsQuadratic EquationActual

, , are the roots of the equation x^3+3 x^2-10 x-24= 0 . If ( + ), ( + ) and ( + ) are the roots of the equation x^3+p x^2+q x+r=0 , then q=

Options

  1. A-44
  2. B-28
  3. C44
  4. D28

Correct answer

D. 28

Step-by-step solution

Since, , , be the roots of the equation aligned & x^3+3 x^2-10 x-24=0 & + + =-10, =24, + + =-3 aligned Now, ( + + )^2= ^2 ^2+ ^2 ^2+ ^2 ^2 ^2 ^2+ ^2 ^2+ ^2 ^2=244 +2 ( + + ) aligned & Since, q= ( + )( + )+ ( + )( + ) & + ( + )( + ) & = ( + + )+ ^2 ^2+ ( + + ) & + ^2 ^2+ ( + + )+ ^2 ^2 & =3 24 (-3)+244=-216+244=28 . aligned

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