+1274 Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.
+1926 First, let's combine all like terms. We get
\(-15x^2-kx+45\)
In order for the solutions not to be real, the descriminant must be less than 0 (negative number).
We have
\((-15)^2 - 4(-k)(45) < 0 \\ 225+180k<0\\ k<-1.25\)
Therefore, the largest integer must be -2.
Thanks! :)
+1926 First, let's combine all like terms. We get
\(-15x^2-kx+45\)
In order for the solutions not to be real, the descriminant must be less than 0 (negative number).
We have
\((-15)^2 - 4(-k)(45) < 0 \\ 225+180k<0\\ k<-1.25\)
Therefore, the largest integer must be -2.
Thanks! :)
