Which real numbers are zeros of the function? f(x)=2x4−9x3+7x2+6x

-1/2, 0, 2, and 3 are the answers

 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