Quadratic equation

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A Quadratic equation is an equation in which an independent variable appears with an exponent of two and no higher exponent. For example,

  • 0 = 2 + 3x + 5x2

A quadratic equation has two roots (i.e. solutions).

The roots of quadratic equation a x2 + b x + c = 0 whose coefficients are real numbers may be categorised as follows:

  • If b2 > 4 a c the roots are real, but different.
  • If b2 = 4 a c the roots are real, and equal.
  • If b2 < 4 a c the roots are complex conjugate pairs (i.e. one root is y + i z, the other y - i z, where i is the complex number which satisfies i2 = -1