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avatar+189 

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

 Jun 11, 2024
 #1
avatar+1334 
+1

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! :)

 Jun 11, 2024

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