SOLUTION: Write a quadratic equation for the solutions x=9 and x=27 Write a quadratic equation for the solutions x=4 and x=16

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write a quadratic equation for the solutions x=9 and x=27 Write a quadratic equation for the solutions x=4 and x=16       Log On


   

Question 560583: Write a quadratic equation for the solutions x=9 and x=27

Write a quadratic equation for the solutions x=4 and x=16
Thank You
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

x=9 or x=27 Start with the given solutions.


x-9=0 or x-27=0 Get everything to one side so that only 0 remains on the right side (for both equations).


%28x-9%29%28x-27%29=0 Use the zero product property to combine the equations.


x%5E2-36x%2B243=0 FOIL out the left side.


So the answer is x%5E2-36x%2B243=0


To check your work, simply solve x%5E2-36x%2B243=0 for x. Doing so will show you that the solutions are x=9 or x=27, which confirm the answer.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+=+9+
+x+=+27+
rewrite these as:
+x+-+9+=+0+
+x+-+27+=+0+
and
+%28+x+-+9+%29%2A%28+x+-+27+%29+=+0+
+x%5E2+-+36x+%2B+243+=+0+
+f%28x%29+=+x%5E2+-+36x+%2B+243+
----------------------
+%28+x+-+4+%29%2A%28+x+-+16+%29+=+0+
+x%5E2+-+20x+%2B+64+=+0+
+f%28x%29+=+x%5E2+-+20x+%2B+64+