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.

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.