Why isn't there a polynomial function with zeroes 0 & 4?

[kismay]

I need help figuring out a quick question from my math homework. It asks me to explain why there isn't a unique polynomial function that has zeroes of 0 and 4. I would appreciate any and all help, since I'm really struggling in math right now.
Thanks in advance!

 

[stapel]

I need help figuring out a quick question from my math homework. It asks me to explain why there isn't a unique polynomial function that has zeroes of 0 and 4. I would appreciate any and all help, since I'm really struggling in math right now.
Thanks in advance!

What does it mean for a polynomial to have a zero? What does this mean graphically? (Hint: Think about the graph and the x-axis.)

If you take, say, a quadratic that has two particular x-intercepts, and then you multiply that quadratic's expression by, say, 2, will the x-intercepts move at all?

If you're still stuck, please reply with your answers to the above. Thank you!

 

[Harry_the_cat]

I need help figuring out a quick question from my math homework. It asks me to explain why there isn't a unique polynomial function that has zeroes of 0 and 4. I would appreciate any and all help, since I'm really struggling in math right now.
Thanks in advance!

Going by the title of your post, I think you might have missed the importance of the word "unique". The question isn't asking "Why isn't there a polynomial function with zeroes 0 & 4?" but rather why there isn't only one such function.