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If two quantities multiply to get zero, does a = 0 or b = 0? or both?

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For example:

When these expressions are expanded, they take on the General Form of quadratics:

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Suppose m and n are numbers such that

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In other words, given the general form of a quadratic equation

if a = 1,

-b = sum of the roots of the quadratic polynomial

c = product of the roots of the quadratic polynomial

which is the same as (keeping in mind that a = 1)

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Therefore, the given quadratic equation can be thought of as

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Completing the Square

Earlier we talked about square quadratic polynomials of the forms (x + α)(x + α) and how these expand to become of the general form:

The roots of the quadratic polynomial above are - and - from

which means that

The above is easy to solve, by taking the square root of both sides of the equation such that

which means that

but since a quadratic polynomial must have 2 roots, we say that

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is now of the same form as

and can easily be factored as

Thus we end up with

The third step is to find the square root of both sides of the equation:

to end up with

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