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AP EAMCET2009MathematicsQuadratic Equation

The roots aligned & (x-a)(x-a-1)+(x-a-1)(x-a-2) & +(x-a)(x-a-2)=0, a R are always aligned

Options

  1. Aequal
  2. Bimaginary
  3. Creal and distinct
  4. Drational and equal

Correct answer

C. real and distinct

Step-by-step solution

Given, aligned & (x-a)(x-a-1)+(x-a-1)(x-a-2) & +(x-a)(x-a-2)=0 aligned Let x-a=t , then t(t-1)+(t-1)(t-2)+t(t-2)=0 array lc & t^2-t+t^2-3 t+2+t^2-2 t=0 & 3 t^2-6 t+2=0 & t= 6 36-24 2(3) = 6 2 3 2(3) & x-a= 3 3 3 & x=a+ 3 3 3 array Hence, x is real and distinct.

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