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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:


Usually the following is defined:


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


That means the graph crosses the x-axis twice.

The equation has one root when


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

And it has no real roots when


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

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


Press here for exercises and solutions in quadratic equations

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