SOLUTION: please help. write the equation of the root 6,-2/3 thanks for your help

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: please help. write the equation of the root 6,-2/3 thanks for your help      Log On


   

Question 140846: please help. write the equation of the root
6,-2/3 thanks for your help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Since 6 and -2%2F3 are given zeros this means that:


x=6 and x=-2%2F3


Get all terms to the left side in each case


x-6=0 and 3x%2B2=0


Now use the zero product property in reverse to join the factors.


%28x-6%29%283x%2B2%29=0


Expand and multiply

3%2Ax%5E2-16%2Ax-12=0


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Answer:

So the polynomial with roots of 6 and -2%2F3 is

3%2Ax%5E2-16%2Ax-12



Notice how if we graph y=3%2Ax%5E2-16%2Ax-12, we can visually verify our answer

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3%2Ax%5E2-16%2Ax-12+%29+ Graph of y=3%2Ax%5E2-16%2Ax-12 with roots of x=6 and x=-2%2F3