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

 Feb 27, 2022

Rearrange the equation, x- 6x + k = 0 , then solve using the quadratic formula.
You will realise that the only possibility for x to be real is when the term under the square root (b- 4ac) must be greater than or equal to 0, so you do not get a negative result under the square root (which makes it imaginary).

You may read more on "discriminants" for more information.

 Feb 27, 2022

ok, so

6x - x^2 = k

everytime x is increased by 1, 6x is increased by 6

everytime x is increased by 1, x^2 is increased by 2x+1, since,




so we added 2x+1


I'll let you figure this out 




p.s also trial and error will work just as fine

 Feb 27, 2022

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