04-3b+Finding+Zeroes+Algebraically

Finding Zeroes Algebraically

We can also find the zeroes of a quadratic equation using algebraic methods.

To find the zeroes of a function, we set the function equal to zero; the solutions to this equation are the zeros of the function.

//**This is not the same thing as evaluating the function when x = 0; doing that will only find the value of y when x equals zero, not the value of x when y equals zero.**// The solutions to a quadratic equation in standard form are called roots; the **//roots//** of an equation are the values of the variable that make the equation true.
 * Notice this: Functions have zeroes or x-intercepts. Equations have solutions or roots.**

We can find the roots of the equations by factoring and applying the Zero Product Property; remember, this property states that if the product of two quantities is zero, at least one of the quantities must equal zero.

So, if we factor a quadratic equation, we end up with two binomials. We can set each of the binomials equal to zero in turn, and solve for the variable.

Factoring, as you might have already noticed, is an art, not a science. No one can actually tell you exactly what to do when factoring; familiarity with the multiplication tables is extremely helpful, as is intuition. The only advice I have is to practice, practice and practice again. After a while it wil become pretty instinctive, but it is one of those dark arts that you'll have to work through.

Proceed to Binomials and Trinomials