The function p(x)= x+1 x^ 2 -5x+1 has a denominator whose real zeros are irrational.
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
The function
p(x)=x2−5x+1x+1
has a denominator whose real zeros are irrational.
(a) Solve x2−5x+1=0 and provide decimal approximations of the roots correct to three decimal places.
(b) For each root found in part (a), calculate the corresponding left–hand and right–hand limits of p(x) as x approaches that root. Clearly indicate whether the function approaches +∞ or −∞ on each side.
(c) Summarize your findings by constructing a sign chart for p(x) on the real line, labeling each interval with the sign of p(x) and marking all vertical asymptotes.