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AP EAMCET2008MathematicsQuadratic Equation

If + =-2 and ^3+ ^3=-56 , then the quadratic equation whose roots are and is

Options

  1. Ax^2+2 x-16=0
  2. Bx^2+2 x+15=0
  3. Cx^2+2 x-12=0
  4. Dx^2+2 x-8=0

Correct answer

D. x^2+2 x-8=0

Step-by-step solution

Given that, + =-2 and ^3+ ^3=-56 array rlrl & & ( + ) ( ^2+ ^2- ) & =-56 & ^2+ ^2- & =28 array aligned Now, & & ( + )^2 & =(-2)^2 & & ^2+ ^2+2 & =4 & & 28+3 & =4 & & & =-8 aligned Required equation is array rlrl & & x^2-(-2) x+(-8) & =0 & x^2+2 x-8 & =0 array

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