The real zeroes of the function f(x) are
Step-by-step explanation: We are given to find the real numbers that are zeroes of the following functions :
We know that
the zeroes of a polynomial function y = p(x) are given by p(x) = 0.
So, the zeroes of the given polynomial (i) are
So, one of the real zeroes of f(x) is x = 0 and the other zeroes are given by
Factor theorem : If at x = a, the value of a function p(x) is zero, then (x-a) is a factor of p(x).
Let us consider that
At x = 1, we have
At x = 2, we have
So, (x-2) is a factor of g(x).
Therefore, we get
That is, the other two zeroes are given by
Since all the four zeroes are real, so all the real zeroes of f(x) are
Thus, the real zeroes of the function f(x) are