Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions

siIviajendeukie Aug 4, 2024

#1**+1 **

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! :)

NotThatSmart Aug 4, 2024