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AP EAMCET202315 May 2023Morning ShiftMathematicsQuadratic EquationActual

If -1 is a twice repeated root of the equation a (x^3+x^2 )+ bx + c =0 , then a : b : c =

Options

  1. A:-1: 1
  2. B-1: 1: 1
  3. C1: 1:-1
  4. D1: 1: 1

Correct answer

B. -1: 1: 1

Step-by-step solution

Since x=1 is a twice repeated root of f(x)=a x^3+a x^2+b x+c=0 . Hence f(-1)=0 and f^ (-1)=0 Now f(-1)=0 -a+a+b+c=0 c=b Now f^ (x)=3 a x^2+2 a x+b aligned & f^ (-1)=3 a-2 a+b & a+b=0 & a=-b & a: b: c=(-b):(b):(b) & =-1: 1: 1 aligned

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