True or false question about algebra

victoria0212

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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

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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

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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

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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

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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

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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.
 
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