What is the largest value of k such that the equation 6x - x^2 = k has at least one real solution?
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. –x2 + 6x – k = 0
Multiply both sides by –1 to get that pesky negative off the x2 x2 – 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 x2 – 6x + 9 = 0
This will factor to (x – 3)(x – 3)
