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

Guest Jan 8, 2021

#1**0 **

Hi Guest!

**Background**

To solve this question, we should use the quadartic equation.

If you don't know what that is, here's a wiki page: https://en.wikipedia.org/wiki/Quadratic_equation

Whether or not a quadratic has a real answer is based on it's discriminant, b^2 - 4ac.

If the discriminant is negative, then the solutions won't work since you can't square root a negative number.

**Equation**

6x - x^2 = k

x^2 - 6x + k = 0

**Discriminant**

b^2 - 4ac

(-6)^2 - 4(1)(k)

36 - 4k

**Solving**

So, we're looking for the greatest k value where 36 - 4k is non-negative.

The smallest non-negative number is 0.

36 - 4k = 0

36 = 4k

k = 9

**Answer**

Thus, our answer is 9.

I hope this helped. :))))

=^._.^=

catmg Jan 8, 2021