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→Quadratic formula: Add examples
</math>
</math>
To use it simply substitute in for the different values of ''a, b'' and ''c''. If the quadratic equation you want to solve has unusual numbers or even algebraic expressions for any of ''a, b'' or ''c'', this is likely the fastest and easiest way to solve it.
To use it simply substitute in for the different values of ''a, b'' and ''c''. If the quadratic equation you want to solve has unusual numbers or even algebraic expressions for any of ''a, b'' or ''c'', this is likely the fastest and easiest way to solve it.
====Examples===
First consider:
:<math>
3x^2 - 25x + 7
</math>
Substituting for ''a, b'' and ''c'' into the quadratic formula we get,
:<math>
x = \frac{- (-25 ) \pm \sqrt{(-25)^2 - 4 \times 3 \times 7}}{2 \times 3}
</math>
Performing some simplifying this is just,
:<math>
x = \frac{25 \pm \sqrt{541}}{6}
</math>
Therefore the solutions are:
:<math>
x = \frac{25 +\sqrt{541}}{6}, \, \frac{25 -\sqrt{541}}{6}
</math>
Now consider the following quadratic,
:<math>
x^2 + 4 = 0
</math>
Applying the quadratic formula gives the solutions to be,
:<math>
x = \frac{0 \pm \sqrt{0^2 - 4 \times 4}}{2} = \frac{\sqrt{-16}}{2}
</math>
The number in the square root is negative meaning the solution to the quadratic will be [[complex number|complex]]. Since,
:<math>
\sqrt{-16} = \sqrt{16} \times \sqrt{-1} = 4 \times \mathrm{i}
</math>
the solution to the quadratic is,
:<math>
x = 2\mathrm{i}, \, x=-2\mathrm{i}
</math>
== References ==
== References ==