+2653 Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 13x^2 + 39 = 0
has no real solutions.
+1926 First, let's set up a quadratic equation for x. Combining some like terms, we get
\(-8x^2-kx+47=0\)
Now, in order for the problem to have no real solutions, the descriminant must be less than 0.
Thus, let's set up the descriminant to find k.
We get that
\(k^2+1504<0\)
Isolating k, we get
\(k^2<-1504\)
However, note that k^2 cannot be negative, meaning that k^2 cannot possibly be smaller than -1504.
Therefore, it is impossible for the equation to have no real solutions.
Thanks! :)
