If r is a double root of a degree 4 polynomial, then results on its coefficients
Source: CMI 2023 B3
May 9, 2023
algebrapolynomialCMI
Problem Statement
Consider the polynomial p(x)=x4+ax3+bx2+cx+d.
It is given that p(x) has its only root at x=r i.e p(r)=0.
<spanclass=′latex−bold′>(a)</span> Show that if a,b,c,d are rational then r is rational.
<spanclass=′latex−bold′>(b)</span> Show that if a,b,c,d are integers then r is an integer.
(Hint: Consider the roots of p′(x) )