Thread: 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!

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 then you will also have root at . At least you will if your polynomial is to have rational coefficients.

-Dan