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avatar+479 

Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

 Jul 22, 2024
 #1
avatar+1918 
+1

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! :)

 Jul 22, 2024
edited by NotThatSmart  Jul 22, 2024
 #2
avatar+129852 
0

No, your answer is  correct, NTS.

 

It's impossible for the discriminant to be < 0

 

Good job!!!

 

cool cool cool

CPhill  Jul 22, 2024
 #3
avatar+1918 
+1

Thanks for the confirmation, CPhill. 

 

:) :) ;)

NotThatSmart  Jul 22, 2024
edited by NotThatSmart  Jul 22, 2024

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