SOLUTION: Determine the nature of the solutions of the equation X2-3x+9=0 A: one real solution B: two non-real solutions C: two real solutions

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Question 374365: Determine the nature of the solutions of the equation X2-3x+9=0
A: one real solution
B: two non-real solutions
C: two real solutions

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The fastest way to answer this question uses the discriminant, b%5E2+-+4ac, with the a, b and c coming from ax%5E2%2Bbx%2Bc. If this expression is:
  • zero, then there is one real solution.
  • positive, then there are two real solutions
  • negative, then there are two complex (non-real) solutions

For x%5E2-3x%2B9 the discriminant is:
%28-3%29%5E2-4%281%29%289%29
which simplifies as follows:
9-4(1)(9)
9-36
-27
This is negative so there are two complex (non-real) solutions.