Question

Produce a third degree polynomial that has exactly the roots -3 and 5 with y-intercept 1350.

I understand I could start with (x+3)(x-5)^2, but i don't know how to get the y-intercept 1350 with the same conditions. Please help. thank you.

Answer 1

We don't know that 5 is a double root. So,

y = (x+3)(x-5)(x-k) = <powers of x> + 15k

So, since the y-intercept is where x=0, all the <powers of x> go away and we have 15k = 1350
k = 90

y = (x+3)(x-5)(x-90)