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NDA2022MathematicsQuadratic EquationActual

If the roots of the equation x^2-a x-b x-c x+b c+c a=0 are equal, then which one of the following is correct?

Options

  1. Aa+b+c=0
  2. Ba-b+c=0
  3. Ca+b-c=0
  4. D-a+b+c=0

Correct answer

C. a+b-c=0

Step-by-step solution

Since x^2-(a+b+c) x+b c+c a=0 has equal roots aligned & [-(a+b+c)]^2-4.1(b c+c a)=0 & [(a+b)+c]^2-4 c(a+b)=0 & (a+b)^2+c^2+2 c(a+b)-4 c(a+b)=0 & (a+b-c)^2=0 & a+b-c=0 aligned

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