Answer:
[tex]\boxed {\boxed {\sf -63}}[/tex]
Step-by-step explanation:
The discriminant is the portion of the Quadratic Formula that is under a square root. It helps us identify if a function has 2,1, or 0 solutions.
The quadratic formula is:
[tex]{x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}[/tex]
where the quadratic is: ax²+bx+c
The part under the square root is just:
[tex]b^2-4ac}[/tex]
We are given the quadratic:
x² -3x+18
Therefore,
- a= 1 (there is an implied coefficient of 1 in front of the x²)
- b= -3
- c= 18
Substitute the values into the formula for the discriminant.
[tex](-3)^2-4(1)(18)}[/tex]
Solve the exponent.
[tex]9-4(1)(18)}[/tex]
Multiply.
[tex]9-72[/tex]
Subtract
[tex]-63[/tex]
Since the discriminant is negative, there are no real solutions. There are imaginary solutions though.
