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

Guest Oct 25, 2022

#2**0 **

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

Let's rearrange 6x - x^2 = k to standard quadratic equation form. –x^{2} + 6x – k = 0

Multiply both sides by –1 to get that pesky negative off the x^{2} x^{2} – 6x + k = 0

What two numbers can we add together to get 6?

There are 5 + 1, 4 + 2, and 3 + 3.

What do we get when we multiply each of those pairs together?

There are 5•1=5, 4•2=8, and 3•3=9.

9 is the largest, so let's say that **k = 9**. Now we have x^{2} – 6x + 9 = 0

This will factor to (x – 3)(x – 3)

Guest Oct 25, 2022