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AP EAMCET202124 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

The equations x^2-a x+b=0 and x^2+b x-a=0 have a common root, then

Options

  1. Aa=b
  2. Ba+b=1
  3. Ca+b=0 or a-b=1
  4. Da-b=2

Correct answer

C. a+b=0 or a-b=1

Step-by-step solution

Equation x^2-a x+b and x^2+b x-a have a common root. Let be the common root of both quadratic equations aligned & ^2-a +b=0 & ^2+b -a=0 aligned Using cross-multiplication gathered ^2 -a b = b 1 = 1 1-a b-a -a 1 1 b ^2 a^2-b^2 = b+a = 1 b+a gathered We get b+a = 1 b+a =1 Now, using first two fraction array rlrl & & 1 a^2-b^2 & = 1 a+b & & a+b & =a^2-b^2 & & (a+b) & =(a+b)(a-b) & & (a+b)(a-b-1) & =0 & a+b=0 or a-b-1 & =0 a-b=1 array

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