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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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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f%28x%29=x%5E2%2B3kx%2B2k%5E2 Start with the given function


f%282%29=%282%29%5E2%2B3k%2A%282%29%2B2k%5E2 Replace every x with 2


f%282%29=4%2B6k%2B2k%5E2 Simplify


0=4%2B6k%2B2k%5E2 Replace the "f(2)" with 0


0=2k%5E2%2B6k%2B4 Rearrange terms


2k%5E2%2B6k%2B4=0 Flip the equation


2%28k%5E2%2B3k%2B2%29=0 Factor out the GCF 2


%282%28k%5E2%2B3k%2B2%29%29%2F2=0%2F2 Divide both sides by 2


k%5E2%2B3k%2B2=0 Simplify


%28k%2B1%29%28k%2B2%29=0 Factor the left side


k%2B1=0 or k%2B2=0 Use the zero product property. Then isolate k for each equation.


k%2B1-1=0-1 or k%2B2-2=0-2


k=-1 or k=-2


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So the values of k are k=-1 or k=-2