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← Rooting out the Solution - College Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. I decided that I'd like to switch what was on either side of the equation just
  2. because I prefer to have x on the left side of the equation. This is just a
  3. personal preference. It doesn't change the math that we're doing at all. I also
  4. set y equal to 0 since we are, after all, looking for the roots of this
  5. equation. Now, what we notice here is that you can actually factor this
  6. expression on the left. X squared plus 8x plus 16 Is just equal to the quantity
  7. x plus 4 times the quantity x plus 4 well these two factors are clearly both
  8. going to give us the same root since they are equal to each other, so from this
  9. we just get one equation x plus 4 equals 0 that needs to be satisfied in order
  10. for this equation to be satisfied Fine. So we get a root of x equals negative 4.
  11. Now even though we only got one answer here for x, we must notice that the
  12. factor that this came from appears twice in the equation. So it's not so much
  13. that there's just one solution, it's that the two roots of this parabola happen
  14. to be identical to one another. In fact this root is so special that it gets a
  15. special name. It's called a double root.