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Quadratic formula

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

 

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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

 

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Example 1

You can see that x² + 2x – 15 = (x – 3)(x + 5), because

And we could have found that by trial and error.

 

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

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