+467 Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.
+1786 First, let's note that if there are no real solutions, then that means the descriminant is less than 0,
Simplifying the quadratic equation a bit, we find that
\(-15x^2-kx+53=0\)
Since the descriminant is b^2-4ac, we have the equation
\(k^2+3180<0\)
This yields \(k^2<-3180\)
Note that this isn't possible. k^2 must be greater or equal to 0, so it cannot be equal to -3180.
I might have done something wrong...not sure, but I think it's impossible
Thanks! :)
+129820 No, your answer is correct, NTS.
It's impossible for the discriminant to be < 0
Good job!!!
