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Factorization
You can factorize a quadratic equation to obtain the zeroes
Explanation
We start with
You can also write this as
To solve the square we will develop a binomial formula
and get
That delivers
The quadratic formula is usually written as
Example 1
The number φ (phi) can be calculated as
For the positive solution you get
and for the (invalid) negative solution you get
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Example 2
You can easily see the zeroes of the parabola x2 + 2x − 15 = 0, but of course you can calculate them