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AP EAMCET202421 May 2024Evening ShiftMathematicsQuadratic EquationActual

If is a common root of x^2-5 x+ =0 and x^2-8 x-2 =0( 0) and , are the other roots of them, then + + + =

Options

  1. A0
  2. B-1
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

is root of x^2-5 x+ =0 and x^2-8 x-2 =0 ^2-5 + =0 ...(i) and ^2-8 -2 =0 ...(ii) Subtracting (ii) from (i), we get 3 +3 =0 =- As is root of x^2-5 x+ =0 aligned & ^2+5 + =0 ^2+6 =0 =-6[ 0] & a=6 aligned Now, , are roots of x^2-5 x+(-6)=0 + =5 =-1 And, , are roots of x^2-8 x+12=0 + =8 =2 So, + + + =6-1+2-6=1 .

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