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

 Jul 31, 2020
 #1
avatar+28021 
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For no real solutions, the discriminant needs to be NEGATIVE

 

b^2 - 4ac <0       b = k    a = 5     c = 8

 

k^2 - 4(5)(8) <0

k^2 < 160

k <   12.65       so the largest INTEGER would be 12

 Jul 31, 2020
 #2
avatar+90 
0

gee thanks ;)

 Jul 31, 2020

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