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Quadratic formula

With the quadratic formula you can factorize a quadratic equation to obtain the roots

 


Explanation

We start with the general form

and separate a with brackets

For the square we are going to prepare a binomial formula

and write this as

The term with an x is handled separately

Here you can calculate two solutions

The quadratic formula is normally written as

 


Example 1

This yields x2 + 2x – 15 = (x – 3)(x + 5) and we could have found that by trial and error.

 


History

The Indian mathematician and astronomer Brahmagupta described this formula in 628.


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