Question

3x^2-3x+4=0
I have to find the discriminant: which is -39 but then I have to determine the type of solutions of the quadratic equation, then solve using the quadratic equation.

Answer 1

here's a table that may be handy

http://www.mathwords.com/d/discriminant_quadratic.htm

Answer 2

in this case, D = -39

Answer 3

Yes, I did get that. I mentioned that in my question....
When I put it in the quadratic equation, is 3 going to be negative or positive since I have to plug a -3 into a -b?

Answer 4

I ended up with x=+ or - the square root of -39 all over 6, but then I get confused

Answer 5

?

Answer 6

\[
x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-(-3) \pm \sqrt{-39}}{2*3} =
\frac{3 \pm \sqrt{-39}}{6} = \frac 12 \pm \frac{\sqrt{39}i}{6}
\]

Answer 7

as the table and aum point out, you'll get a complex solution since D = -39 which is less than 0.

Answer 8

2 complex solutions I mean

Answer 9

\[i = \sqrt{-1}\]

Answer 10

I understand everything except for the last part...why is i suddenly added in

Answer 11

You cannot take the square root of a negative number. This is because x^2 is never negative.

To get around the fact that x^2 = -1 has no real solutions, the idea that \[i = \sqrt{-1}\] was introduced. This is known as an imaginary number. Using this notation, x^2 = -1 now has a solution which is a complex number.

Answer 12

the solutions to x^2 = -1 are x = i or x = -i

Answer 13

Thank you very much for your help. I highly appreciate the tutoring.