Question #aa189 Algebra Properties of Real Numbers Properties of Rational Numbers 1 Answer Ratnaker Mehta Apr 12, 2017 #k=0.# Explanation: #p(x)=x^2-x-2.# To find #k#, such that, #AA x,p(x+k)=p(x-k).# Now, #p(x+k)=p(x-k),# #rArr (x+k)^2-(x+k)-2=(x-k)^2-(x-k)-2,# #rArr x^2+2kx+k^2-x-k-2=x^2-2kx+k^2-x+k-2,# #rArr 4kx-2k=0, or, 2k(2x-1)=0# #rArr k=0.# Answer link Related questions What are Rational Numbers? How are rational numbers related to integers? How do you simplify rational numbers? What are the properties of Rational Numbers? What is the difference between proper and improper fractions? How do you order fractions from least to greatest? How do you determine which fraction is greater 3/7 or 4/9? How do you simplify the fraction 10/20? How do you order 11/12, 12/11, 13/10 from least to greatest? Question #ba7ff See all questions in Properties of Rational Numbers Impact of this question 1391 views around the world You can reuse this answer Creative Commons License