SOLUTION: 3x^2-5x+4 I don't understand how to plot this parabola. I end up getting a +- 5 sqrt -23/6 using quadratic formula.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 3x^2-5x+4 I don't understand how to plot this parabola. I end up getting a +- 5 sqrt -23/6 using quadratic formula.      Log On


   

Question 344800: 3x^2-5x+4
I don't understand how to plot this parabola. I end up getting a +- 5 sqrt -23/6 using quadratic formula.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
re: Your question
so I still don't understand how online calculators are getting x= 0.83333 +- 0.79930i. Where does the .83333 come from? "I understand that root(-23) = .79930i, but cannot figure out .83333"
.
online calculators are following thru with the division by the 6 in the denominator
-(-5)/2*3 or 5/6 is .83333
sqrt(-)23*i /2*3 = +-4.79583*i /6 = +-.79930i
.
Hi, it does end up with a square root of a negative number(-23): See below:
That means there are no solutions among real numbers.
3x%5E2-5x%2B4
.
Using Quadratic Formaula to solve:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A3%2A4=-23.

The discriminant -23 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -23 is + or - sqrt%28+23%29+=+4.79583152331272.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B4+%29