+280 Find the largest integer k such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.
+1926 First, we need to simplify the equation, so let's combine all the like terms.
We get \(-15x^2-kx+45\)
Now, in order for the solutions to be nonreal, the descriminant must be less than 0.
The descriminant is \(b^2-4ac\), so plugging in our values, we get
\((-15)^2 - 4(-k)(45) < 0 \\ 225+180k<0\\ k<-1.25\)
Therefore, the biggest interger k can be is -2.
So -2 is our answer!
Thanks! :)
