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

 Jun 8, 2024

Best Answer 

 #1
avatar+759 
+1

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! :)

 Jun 8, 2024
edited by NotThatSmart  Jun 8, 2024
 #1
avatar+759 
+1
Best Answer

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! :)

NotThatSmart Jun 8, 2024
edited by NotThatSmart  Jun 8, 2024

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