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Quadratic equation

Revision as of 13:23, 27 June 2006 by B-flat (talk | contribs) (→‎Factoring)

Quadratic Equations

A quadratic equation is an equation of form ${a}{x}^2+{b}{x}+{c}=0$. a, b, and c are constants, and x is the unknown variable. Quadratic Equations are solved using 3 main strategies: factoring, completing the square, and the quadratic formula.

Factoring

The purpose of factoring is to turn a general quadratic into a product of binomials. This is easier to illustrate than to describe.

Example: Solve the equation $x^2-3x+2=0$ for x.

Solution: $x^2-3x+2=0$

First we expand the middle term. This is different for all quadratics. We cleverly choose this so that it has common factors. We now have $x^2-x-2x+2=0$.

Next, we factor out our common terms to get: $x(x-1)-2(x-1)=0$. We can now factor the (x-1) term to get: $(x-1)(x-2)=0$. By a well known theorem, either $(x-1)$ or $(x-2)$ equals zero.

We now have the pair of equations x-1=0, or x-2=0. These give us answers of x=1 or x=2. Plugging these back into the original equation, we find that both of these work! We are done.

Completing the square

Completing the square

Quadratic Formula

See Quadratic Formula.

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