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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 20, 2024
 #1
avatar+129725 
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Simplify as

 

-15x^2 -kx + 53 = 0

 

This will have no real solutions when the discriminant is < 0

 

k^2 - (4)(53)(-15)  < 0

 

k^2 + 3180 < 0

 

k^2 + 3180  is always >  0.....so no value of "k" will give us non-real solutions

 

cool cool cool

 Jun 20, 2024

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