Algebra

Simplify to... 3x^2 - kx + 33 = 0

Then in Desmos, graph 

3x^2 - kx + 33 = 0

and

k = 0

Click on k = 0 and set the Step to 1

Change the range from "-10 to 10" to "0 to 25"

let the slider play from 25 to 0 and find the first one that has no line shown on it

First, let's simplify and combine all like terms. 

After doing that, we get

\(3x^2-kx+33=0\)

 

Now, in order for the equation to have no real solutions, the descriminant must be less than 0. 

The descriminant is \(b^2-4ac\), so we have the equation

 

\(k^2 - 4(33)(3) < 0\)

Since we are trying to find the largest, we set the two to equal each other and get

 

\(k^2 - 396 = 0\\ k^2 = 396\\ k \approx 19.89974\)

 

Rounding down, the largest k can be as an integer is 19. 

So our answer is 19. 

 

Thanks! :)