Question

f(x) = x ^ 2 + ax + bf(x) has m zeros, and f[f(x)] has M zeros,So M - m will never be ____A. 0B. 1C. 2D. 3

Answer 1

First, notice that the expression for f(f(x)) is the following:

`f(f(x))=(x^2+ax+b)^2+a(x^2+ax+b)+b`

notice that the first term is a quadratic expression with exponent 2. This means that f(f(x)) has 4 zeros.

Since f(x) has 2 zeros (since its quadratic), we have that M-m = 4-2 = 2, thus, M-m will never be 0, 1 or 3