Discriminant of Quadratic Equation/Also presented as

Discriminant of Quadratic Equation: Also presented as

While the discriminant $\Delta$ of a quadratic equation $\QQ: a x^2 + b x + c = 0$ is properly given as:

$\map \Delta \QQ = \dfrac {b^2 - 4 a c} {a^2}$

it is usual and practically universal that $\map \Delta \QQ$ is given as:

$\map \Delta \QQ = b^2 - 4 a c$

This is because we are usually interested only in the sign of $\map \Delta \QQ$ and not its actual value.

Indeed, we note that as $a^2 > 0$, multiplying or dividing by $a^2$ has no effect on that sign.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): discriminant (of a polynomial equation)
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): discriminant (of a polynomial equation)
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