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← Non negative Discriminants - College Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. Here's our quadratic formula written out once again, and I've written the
  2. discriminant b squared minus 4ac in teal. It's important to note that we're
  3. taking the square root of this number, and as we've said many times before, we
  4. only know how to take the square root of non-negative numbers, non-negative real
  5. numbers to be exact. So if we have a negative number under here, we're not going
  6. to get any real solutions. However, we need to make another distinction among
  7. the numbers that do give us real solutions. If we have a 0 under here, then we
  8. only get 1 real solution. Since we'll have negative b plus or minus 0, and
  9. either adding or subtracting zero from negative b gives us the same number, just
  10. negative b. So we would just get negative b over 2a. If the discriminant is 0.
  11. That's only 1 answer. This is only 1 number. It's our plus or minus, which is
  12. what split this into 2 solutions originally, is no longer doing that for us. If
  13. b squared minus 4ac is positive, then we'll get some real number here and
  14. negative b plus that number will be different from negative b minus that number.
  15. So in that case we will wind up with 2 roots, two positions where we know that
  16. our parabola hits the x axis.