Zeros of a Quadratic Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Find the zeros of g(x)=2x2−8xg(x) = 2x^2 - 8x.

Solution

  1. 1
    Factor out 2x2x: 2x(x−4)=02x(x - 4) = 0.
  2. 2
    Set each factor to zero: 2x=0⇒x=02x = 0 \Rightarrow x = 0; x−4=0⇒x=4x - 4 = 0 \Rightarrow x = 4.
  3. 3
    Zeros: x=0x = 0 and x=4x = 4.

Answer

x=0 and x=4x = 0 \text{ and } x = 4
When there is no constant term, one zero is always x=0x = 0. Factor out xx (or 2x2x) to find the other zero.

About Zeros of a Quadratic

The zeros (or roots) of a quadratic function f(x)=ax2+bx+cf(x) = ax^2 + bx + c are the values of xx where f(x)=0f(x) = 0. Graphically, they are the xx-intercepts of the parabola.

Learn more about Zeros of a Quadratic →

More Zeros of a Quadratic Examples

Example 1 easy

Find the zeros of [formula].

Example 3 easy

Find the zeros of [formula].

Example 4 hard

How many zeros does [formula] have over the reals?

← All Zeros of a Quadratic Examples Zeros of a Quadratic Concept