If Joe has a package of 25 cookies, and he eats 15 of them, what percent of the
1 answer:
You might be interested in
It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.
The simplest polynomial with these characteristics would be
but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with
which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:
Polynomials are linear combinations of positive integer powers. For example,
is a polynomial, but
is not.
(In case you're unfamiliar with the term, a linear combination of two quantities is the sum of scaled versions of those quantities, e.g. a general linear combination of and
is
, where
are any numbers.)
is not a polynomial; the offending term is
, or
.