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Quadratic Formula – Quadratic Equation

When given a quadratic equation:

ax^2+bx+c=0, a\neq 0

The points where the graph intersects the x-axis are called roots or zeros or solutions, which can be easily found with this quadratic formula:

x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Usually the following is defined:

\Delta=b^2-4ac

Then it’s easy to see from the formula that the equation has 2 roots when

\Delta>0

That means the graph crosses the x-axis twice.

The equation has one root when

\Delta=0

Which means the graph crosses the x-axis exactly once.

And it has no real roots when

\Delta<0

And that means the graph doesn’t cross the x-axis at all.

In addition, the roots of the equation also follow these formulas:

x_1+x_2=-\frac{b}{a}

x_1\cdot x_2=\frac{c}{a}

Also, with the roots you can factor the quadratic equation as follows:

ax^2+bx+c=a(x-x_1)(x-x_2)

Press here for exercises and solutions in quadratic equations

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