Quadratic formula

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For the quadratic equation ax2 + bx + c = 0, the real solutions are given by the quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

[edit] Discriminant

The discriminant Δ in the quadratic equation is given by:

Δ = b2 − 4ac

The discriminant can be used to provide information about the number of solutions to a quadratic equation:

[edit] Example

Suppose one needed to find solutions for the equation x2 − 6 = x.

First we rearrange the equation to make it equal zero:

x2 − 6 = x
\therefore x^2-x-6=0

Now, using the quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
a=1, b=-1, c=-6 \therefore x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}
\therefore x=\frac{1\pm\sqrt{25}}{2}=\frac{1\pm5}{2}
\therefore x=\frac{6}{2}=3 or x=\frac{-4}{2}=-2.
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