Zeros to polynomial

[shooter609]

Find a degree 3 polynomial with real coefficients whose leading coefficient is 5 that has -2,1, and 4 as zeros.
Write a polynomial function with real coefficients in standard form whose zeros include -2,3, and 4-5i

 

[JeffM]

Find a degree 3 polynomial with real coefficients whose leading coefficient is 5 that has -2,1, and 4 as zeros.
Write a polynomial function with real coefficients in standard form whose zeros include -2,3, and 4-5i

Please read the rules: http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

 

[HallsofIvy]

Any cubic polynomial can be written in the form r(x- a)(x- b)(x- c) where a, b, and c are the zeros of the polynomial. I suspect your were to have learned that before you were given this problem.

There are an infinite number of answers to the second problem but the simplest is the fourth degree polynomial having -2, 3, 4- 5i, and 4+ 5i as zeros. Do you see why I added "4+ 5i" to the roots you were given?