SOLUTION: Assume that x=2 is a zero of f(x)=x^2+3kx+2k^2 (that is, f(2)=0). Find the value(s) of k. Could you please show the steps and explain how you got there?? This is a question t

Question 1050396: Assume that x=2 is a zero of f(x)=x^2+3kx+2k^2 (that is, f(2)=0). Find the value(s) of k.
Could you please show the steps and explain how you got there??
This is a question to help me better understand what I missed in class the other day; I have a quiz tomorrow! Please help!
Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The idea is to plug in x = 2 and replace f(2) with 0. Then solve for k.

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Start with the given function

Replace every x with 2

Simplify

Replace the "f(2)" with 0

Rearrange terms

Flip the equation

Factor out the GCF 2

Divide both sides by 2

Simplify

Factor the left side

or Use the zero product property. Then isolate k for each equation.

or

or

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So the values of k are or
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