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algebra

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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?

Oct 21, 2022

#1
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x^2-6x+k=0

$$x = {-(-6) \pm \sqrt{(-6)^2-4(1)(k)} \over 2(1)}=3\pm1\sqrt{9-k}$$

If k gets any bigger than 9, there both roots will be zero. Hence the largest value k can be such that that equation has at least one real solution is 9.

Oct 21, 2022