Find a polynomial function that has the given zeros. (There are many correct answers.) 6,4+√7,4-√7

Answer 1

For this one, focus on the matched pair first:

4+sqrt(7), 4-sqrt(7)

I'll call these two roots R and Q

(x-R)(x-Q) = x^2 -Rx -Qx + RQ

The sqrt() parts cancel each other out in the x terms. And in the RQ term, you get 16-7 = 9.

so (x-R)(x-Q) = x^2 - 8x + 9

Then multiply this by the third root:

(x^2 - 8x + 9)(x-6) = x^3 -8x^2 + 9 x

-6x^2 +48 x -54

= x^3 -14 x^2 + 57 x - 54