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Manipal MET2010MathematicsQuadratic Equation

Let a, b, c be real numbers with a 0 and let , be the roots of the equation a x^2+b x+c=0 , then a^3 x^2+a b c x+c^3=0 has roots

Options

  1. A^2 , ^2
  2. B, ^2
  3. C^2 ,
  4. D^3 , ^3

Correct answer

A. ^2 , ^2

Step-by-step solution

Dividing the equation, a^3 x^2+a b c x+c^3=0 by c^2 , we get a ( a x c )^2+b ( a x c )+c=0 a x c = , are roots. x= c a and x= c a x= ^2 and x= ^2 [ = c a . as , are the roots of .a x^2+b x+c=0 ] are roots of above equation.

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