How to write an equation for a rational function with: x intercepts at x = 6 and x = 5?

1 Answer
Dec 30, 2015

Answer:

Start from the factored form to find

#f(x) = x^2 - 11x + 30#

Explanation:

An #x# intercept occurs when #f(x) = 0#. Then, we are just looking for a rational function #f(x)# such that #f(6) = f(5) = 0#. We can easily construct a polynomial with the desired property by starting in factored form.

It should be clear that if #f(x) = (x-6)(x-5)# that plugging in #5# or #6# will give #0#. Then, as a polynomial is certainly a rational function, it satisfies the desired requirements, and so we can just expand to get

#f(x) = x^2 - 11x + 30#