Answer:
f(x) = 2x² +13x -7
Explanation:
Given a root r, a factor of the expression with that root is (x -r). For your roots, the factors of a suitable polynomial are ...
(x -1/2)(x +7)
Since you don't want any fractions, you can multiply this by 2:
(2x -1)(x +7)
And you can eliminate parentheses and write it as a function.
f(x) = (2x)(x +7) -1(x +7) = 2x² +14x -x -7
f(x) = 2x² +13x -7