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Find the largest integer k such that the equation

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

has no real solutions.

 Feb 10, 2022
 #1
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5x^2  -kx  + 8  = 4x^2          .....subtract 4x^2  from both sides

 

x^2  - kx + 8  =  0

 

We will have no solutios  when the discriminant ....   (-k)^2  - 4 (1) (8)  < 0

 

So....simplifying  and rearranging  we have

 

k^2   <   32

 

The integer values  that  make this  true   are  [   -5 ...... 5 ]

 

So.....5  is the largest  integer that produces no real solutions

 

 

cool cool cool

 Feb 10, 2022

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