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AP EAMCET202316 May 2023Evening ShiftMathematicsQuadratic EquationActual

If c and d are the roots of x^2+a x+b=0 , then a root of x^2+(4 c+a) x+ (b+2 a c+4 c^2 )=0 is

Options

  1. Ad+2 c
  2. Bd + c
  3. Cd - c
  4. Dd -2 c

Correct answer

D. d -2 c

Step-by-step solution

Given that c and d are the roots of x^2+a x+b=0 aligned & c+d=-a & c d=b ... (i) & aligned & Now, x^2+(4 c+a) x+ (b+2 a c+4 c^2 )=0 & x^2(4 c-c-d) x+ (b-2 c(c+d)+4 c^2 )=0 & x^2+(3 c-d) x+2 c^2-c d=0 & x^2+c x+(2 c-d) x+c(2 c-d)=0 & (x+c)(x+2 c-d)=0 & x=d-2 c . aligned aligned

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