# How would I find this cubic polynomial function?

• Jan 22nd 2013, 01:11 PM
misiaizeska
How would I find this cubic polynomial function?
"Find the cubic polynomial function with two of its zeros 2 and -3+√2 and a y-intercept of 7."
Answer: y = -0.5(x -2)(x2 + 6x + 7)

I think that the function will look something similar to: y = k(x-2)(x-(-3+√2))2
Then I would use the coordinates of the y-intercept (0,7) to find the value of k. However, I'm not sure how to get "(x2 + 6x + 7)".
Any suggestions would be appreciated, thank you!
• Jan 22nd 2013, 01:26 PM
topsquark
Re: How would I find this cubic polynomial function?
Quote:

Originally Posted by misiaizeska
"Find the cubic polynomial function with two of its zeros 2 and -3+√2 and a y-intercept of 7."
Answer: y = -0.5(x -2)(x2 + 6x + 7)

I think that the function will look something similar to: y = k(x-2)(x-(-3+√2))2
Then I would use the coordinates of the y-intercept (0,7) to find the value of k. However, I'm not sure how to get "(x2 + 6x + 7)".
Any suggestions would be appreciated, thank you!

Hint: If you have a root at $\displaystyle x = -3 + \sqrt{2}$ then you will also have root at $\displaystyle x = -3 - \sqrt{2}$. At least you will if your polynomial is to have rational coefficients.

-Dan