Sketch a cubic function third degree polynomial function y

Sketch a cubic function (third degree polynomial function y = p(x) with two distinct zeros at x = 2 and x - 5 and has a local maximum located at x = 5. Then determine a formula for your function.

Solution

The function is (x-2)(x-5)(5-x)

we are given that 5 is a double root and 2 is also a root.

Now if i take (x-2)(x-5)(x-5) then 5 will not be a local maximum but it will be an local minimum

so we have the answer as

p(x) = (x-2)(x-5)(5-x)