SOLUTION: When are the roots of X^2 + ax + b complex? What does the sketch look like?

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Question 699249: When are the roots of X^2 + ax + b complex? What does the sketch look like?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if you have x%5E2+%2B+ax+%2B+b, compared to general form ax%5E2%2Bbx%2Bc your a=1, b=a and c=b
using quadratic formula you can find roots:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
this part is discriminant, and if discriminant is less than zero, you will have complex roots
in your case discriminant is:
+%28+a%5E2-4%2A1%2Ab+%29%2F%282%2A1%29+ and if it is less than zero, you will have complex roots
Graph has no real roots, it has no x-intercepts, if both roots are complex.