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AP EAMCET202315 May 2023Morning ShiftMathematicsQuadratic EquationActual

If the values of k for which the equation x^2+2(k+2) x+6 k +7=0 has equal roots are k ₁ and k ₂ , then k ₁^2+ k ₂^2=

Options

  1. A8
  2. B9
  3. C10
  4. D12

Correct answer

C. 10

Step-by-step solution

x^2+2(k+2) x+6 k+7=0 has equal roots Hence aligned & b^2-4 a c=0 & . [2(k+2)]^2-4(1)(6 k +7) ]=0 & k=3,1 aligned Hence k₁=3, k₂=1 k₁^2+k₂^2=10

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