# True or false question about algebra

#### victoria0212

##### New member
Is it true or false that one off the roots to this equation (x-2)(x-4)=0 is zero?
Someone please explain what to do. Thanks!

#### Subhotosh Khan

##### Super Moderator
Staff member
Is it true or false that one off the roots to this equation (x-2)(x-4)=0 is zero?
Someone please explain what to do. Thanks!
Please tell us the "definition" of the "roots" of a polynomial function.

#### victoria0212

##### New member
Please tell us the "definition" of the "roots" of a polynomial function.
You just want me to explain the definition? Well, the roots of a polynomial are the values of the variable that cause the polynomial to evaluate to zero.

#### Subhotosh Khan

##### Super Moderator
Staff member
You just want me to explain the definition? Well, the roots of a polynomial are the values of the variable that cause the polynomial to evaluate to zero.
Excellent! That is correct.

Now please tell us:

what is the value of f(x) = (x-2)(x-4)

when you evaluate f(x) at x = 0?

#### hoosie

##### Junior Member
It will make more sense to you if you understand what the solutions to the equation (x - 2)(x - 4) = 0 represent.
Graph the parabola y = (x -2)(x - 4) and identify where the curve crosses the X -axis. How do these x-intercept values compare with the roots of your equation? What would the curve have to do if 0 was a root of your equation?

#### JeffM

##### Elite Member
Hoosie

Your post makes no sense to me whatsoever. The OP understands that

$$\displaystyle a \text { is a root of } f(x) \iff f(a) = 0.$$

So to solve the problem all that is needed, once you remember that definition, is to determine whether it is true or false that

$$\displaystyle (0 - 2)(0 - 4) = 0$$

The problem revolves around applying the definition of root. Graphing a parabola or translating that parabola just complicates unnecessarily what the student could grasp by thinking about a definition the student already knows.