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Find the largest integer k such that the equation

5x^2 - kx + 8 = 4x^2

has no real solutions.

 Jul 10, 2021
 #1
avatar+33621 
+2

re-write as

 

x^2 - kx + 8 = 0          discriminant of Quadratic Formula must be < 0 for no real roots

 

b^2 - 4ac < 0

 

k^2 - 4(1)(8) < 0

k^2 < 32

k  <   sqrt 32         sqrt 32 = 5.65    so largest integer would be 5

 Jul 10, 2021
 #2
avatar+2122 
0

5x^2 - kx + 8 = 4x^2 has no real solution if the discriminant is negative. 

5x^2 - kx + 8 = 4x^2

x^2 - kx + 8 = 0

b^2 - 4ac < 0

(-k)^2 - 4(1)(8) < 0

(-k)^2 < 32

-sqrt(32) < k < sqrt(32)

-4sqrt(2) < k < 4sqrt(2)

 

=^._.^=

 Jul 10, 2021

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