Posted by Nilan on Tuesday, October 4, 2011 at 7:18am.
Produce a third degree polynomial that has exactly the roots 3 and 5 with yintercept 1350.
I understand I could start with (x+3)(x5)^2, but i don't know how to get the yintercept 1350 with the same conditions. Please help. thank you.

Algebra  Reiny, Tuesday, October 4, 2011 at 8:22am
you are only given two roots, so let the equation be
y = (x+3)(x5)(xa)
but you know that (0,1350) lies on it
1350 = (3)(5)(a)
1350 = 15a
a = 90
so equation is
y = (x+3)(x5)(x90)
expand if you have to, it is more useful in factored form.
btw, your equation of y = ....(x5)^2 would have a double root of 5, that is, it would "touch" the xaxis at x = 5