prove that exist positive real numbers $a_{2019},...a_{1},a_{0}$ such that with each other Select sign + or - then polynomial $\pm a_{2019}x^{2019}\pm a_{2018}x^{2018}\pm ...\pm a_{1}x\pm a_{0}$ there are 2019 distinct real root
Example polynomial
$x^2+3x+2$
$-x^2-3x-2$
$x^2-3x-2$
$-x^2+3x+2$
$x^2-3x+2$
$-x^2-3x+2$
$-x^2+3x-2$
$x^2+3x-2$
Alway there are two distinct root.but with $n=2019$ is two big . I don't know any idea ?