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Quadratic Reciprocity, Reciprocal Calculator

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About Reciprocal Calculator

Quadratic reciprocity calculator finds the quadratic equation whose roots are reciprocal to the roots of the equation. It takes the sum and product root of the equations and reciprocate it corresponding roots.

How The Quadratic Reciprocity Works

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The reciprocity of a quadratic equation, below is how it works

  • You are  given an equation in this form ax2 + bx + c = o
  • Find the roots of the equation, only works if the roots are real.
  • Make the root of the equation be p and q
  • Determine the product of the roots by setting p * q  = c / a.
  • Determine the sum of the roots by setting p + q = -b/ a.
  • Reciprocate or invert the roots p and q in this form 1/p and 1/q 
  • Find the product of the reciprocal roots and set this to 1/p * 1/q = a / c.
  • Repeat the same procedure for the sum of reciprocal roots as 1/p + 1/q = -b/ c.
  • Use this formula to redefine or reconstruct the quadratic equation where the sum and product of the roots are known x2 – (Sum of the roots)x + (Product of the roots) = 0.
  • The reciprocity of a quadratic is born

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