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Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions

 Jul 3, 2024
 #1
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Simplify as

 

3x^2 - kx + 33 = 0

 

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

 

So

 

k^2  - 4(3) (33) < 0

 

k^2  - 396 < 0

 

k^2 < 396

 

k < sqrt (396)

 

k = 19

 

cool cool cool

 Jul 3, 2024

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