Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial
p
with complex coefficients has a complex root. However, no analogous result holds for guaranteeing that a real root exists to
p
if we restrict the coefficients to be real. Let
n
≥
1
and
P
n
be the vector space of all polynomials of degree
n
or less with real coefficients. In this article, we give explicit forms of polynomials in
P
n
such that all of their roots are real. Furthermore, we present explicit forms of linear transformations on
P
n
which preserve real roots of polynomials in a certain subset of
P
n
.