Q. 14 Page 28:
"Given that p(x) is a real polynomial of degree <= 4 such that one can find five distinct solutions to the equation p(x) = 5, what is the value of p(5)?" Answer Choices A. 0, B. 1, C. 4, D. 5, E. Cannot be determined.
While solving this question, I was puzzled as to when a polynomial of degree 4 or less can have five DISTINCT roots? The question was absurd to me, so no answer made sense.
The answer at the back of the book states the polynomial must be zero.
So for example p(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e - 5, where all a, b, c, d, e - 5 = 0.
p(1) - 5 = 0 => x = 1 is a root;
p(2) - 5 = 0 => x = 2 is a root...so on.
Therefore, p(5) - 5 = 0, So p(5) = 5.
Isn't it plain nonsense? I mean does a zero polynomial having 5 distinct roots make sense? How about 25,000 distinct roots, 36437 repeated roots, 23123 complex roots,...