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AP EAMCET202315 May 2023Morning ShiftMathematicsQuadratic EquationActual

If the equation x^4+a x^3+b x^2+c x+d=0 has three equal roots, then that root is

Options

  1. A6 c-a b 8 b-3 a^2
  2. Ba b-6 c 8 b+3 a^2
  3. C6 c - ab 3 a ^2-4 ~b
  4. D6 c-a b 3 a^2-8 b

Correct answer

D. 6 c-a b 3 a^2-8 b

Step-by-step solution

Let , , , be the roots of given equation x^4+a x^3+b x^2+c x+d=0 Hence 3 + =-a, 3 ( + )=b ^2( +3 )=-c, ^3 =d Now consider 6 c-a b= (3 ^2-6 +3 ^2 )....(1) also consider 3 a^2-8 b= (3 ^2-6 +3 ^2 )....(2) dividing equation (i) by equation (2), = 6 c-a b 3 a^2-8 b

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