SOLUTION: find all roots and check answer 5x^3 - 8x =12x

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Question 212364This question is from textbook intermediate algebra
: find all roots and check answer 5x^3 - 8x =12x This question is from textbook intermediate algebra

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find all roots and check answer

5x%5E3+-+8x+=12x

Note: Since this is a polynomial of degree 3, it has three roots.

Step 1. Subtract 12x from both sides to make right side of equation = 0

5x%5E3+-+8x-12x+=12x-12x=0

5x%5E3-20x=0

Step 2. Factor out 5x

5x%28x%5E2-4%29=0+

Step 3. Note difference of squares x%5E2-4=x%5E2-2%5E2 where

x%5E2-2%5E2=%28x%2B2%29%28x-2%29

Step 4. The completely factored polynomial is now

5x%28x-2%29%28x%2B2%29=0

Step 5. To make the above equation equal to zero implies each factor be set to zero to find the roots.

Step 5a. 5x=0 implies x=0 and check by substituting x=0 into

5x%5E3+-+8x+=12x yielding 0=0 ok.


Step 5b. x-2=0 implies x=2 and check by substituting x=2 into

5x%5E3+-+8x+=12x yielding 5%282%5E3%29-8%282%29=12%2A2 OR 40-16=24 OR 24=24 ok.

Step 5c. x-2=0 implies x=2 and check by substituting x=2 into

5x%5E3+-+8x+=12x yielding 5%28%28-2%29%5E3%29-8%28-2%29=12%2A%28-2%29 OR -40%2B16=-24 OR -24=-24 ok.

Step 6. So the roots are: 0, 2, and -2.

Hope you understood and followed the steps. Good luck in your studies. Dr J

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