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AP EAMCET201920 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

If ( ) and ( ) are the roots of (x^2+7 x+3=0 ) and ( 2 3-4 , 2 3-4 ) are the roots of (a x^2+b x+c=0 ) and GCD of (a, b, c ) is 1 , then (a+b+c= )

Options

  1. A11
  2. B0
  3. C243
  4. D81

Correct answer

D. 81

Step-by-step solution

( aligned & Let 2 3-4 =y 2 =3 y-4 y & (2+4 y)=3 y = 3 y 2+4 y aligned ) ( ) is root of quadratic equation (x^2+7 x+3=0 ), So, ( aligned & ( 3 y 2+4 y )^2+7 ( 3 y 2+4 y )+3=0 & 9 y^2+84 y^2+42 y+48 y^2+48 y+12=0 & 141 y^2+90 y+12=0 & 47 y^2+30 y+4=0 & y= 2 3-4 is root of quadratic equation & a x^2+b x+c=0 . & a=47, b=30 and c=4 and G C D of 47,30,4 is 1 . & a+b+c=47+30+4=81 aligned ) Hence, option (4) is correct.

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