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What is the largest value of k such that the equation 6x-x^2=k has at least one real solution?

 Jan 9, 2021
 #1
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By the quadratic formula, the largest possible value of k is 12.

 Jan 9, 2021
 #2
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Rewrite as x^2 - 6x + k  = 0

This has at least one real solution as long as the discriminant is greater than or equal to zero.

 

i.e.  6^2 - 4k >= 0

 

4k <= 36

 

k<= 9

 

So largest value of k is 9.

 Jan 9, 2021

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