Real Root Polynomials and Real Root Preserving Transformations
2021 ◽
Vol 2021
◽
pp. 1-5
Keyword(s):
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 .
2018 ◽
Vol 97
(3)
◽
pp. 382-385
Keyword(s):
Keyword(s):
2021 ◽
Vol 15
◽
pp. 86-90
1983 ◽
Vol 35
(1)
◽
pp. 18-27
◽
1988 ◽
Vol 40
(6)
◽
pp. 1301-1314
◽