Question 374365
The fastest way to answer this question uses the discriminant, {{{b^2 - 4ac}}}, with the a, b and c coming from {{{ax^2+bx+c}}}. If this expression is:<ul><li>zero, then there is one real solution.</li><li>positive, then there are two real solutions</li><li>negative, then there are two complex (non-real) solutions</li></ul>
For {{{x^2-3x+9}}} the discriminant is:
{{{(-3)^2-4(1)(9)}}}
which simplifies as follows:
9-4(1)(9)
9-36
-27
This is negative so there are two complex (non-real) solutions.