What is the difference between a factor of a quadratic equation and a zero of a quadratic equation?Â Â

Question

What is the difference between a factor of a quadratic equation and a zero of a quadratic equation?Â Â

shadowfiend · Answer

Generally speaking, a factor is the component of a quadratic equation that gives you a zero.

For example, if you have the quadratic equation $x^2 - 4$, you can *factor* it into two parts:

$$x^2 - 4 = (x + 2)(x - 2)$$

$x + 2$ and $x - 2$ are the *factors*, and they give you the two *zeros*, which are 2 and -2. A zero is the value of x at which the parabola that the quadratic formula describes crosses the y axis (i.e., has a value of 0). A factor is a part of the equation. Multiplying all the factors together gives you the original equation.

anonymous · Answer

Shadowfiend is correct, with one small "oops." The zeros are where the curve of the equation crosses the X-axis, not the y-axis. So in the example above, the parabola crosses the x-axis at 2 and -2; it crosses the y-axis at -4. (The constant term of a polynomial is always the y-intercept.)

shadowfiend · Answer

Hah! Yes indeed, where it crosses the X axis. Thanks for the catch, LBickford :)