Question

If 2 is a zero of a polynomial Q(x) , then 3 is a zero of Q(x-1)

it's true, but how can we justify the answer ??
tysmm

Answer 1

Therefore, we can see that if 2 is a zero of Q(x), then 3 is a zero of Q(x-1).

Explanation:

This statement is true because if Q(x) is a polynomial and 2 is a zero (or a root) of Q(x), then there exists some non-zero coefficient c such that Q(2) = c(2-2)^n = 0, where n is the degree of the polynomial.Since Q(2) = 0, we can say that Q(x) = (x-2)P(x) for some polynomial P(x). Therefore, Q(x-1) = (x-1-2)P(x-1) = (x-3)P(x-1).Since 3 is a root of Q(x-1), this means that there exists some non-zero coefficient d such that Q(3) = d(3-3)^m = 0, where m is the degree of the polynomial P(x).