You can put this solution on YOUR website! Every polynomial in one variable of degree n, n > 0, has exactly n real or complex zeros.
Total zeroes = total no. of roots = degree of the polynomial = highest index = 5
Since the coefficients of the polynomial are real so is there has to be complex roots, that will occur in pairs - at max there can be two pairs of complex and conjugate roots. Hence, there is at least one real root.
To find max no. of negative roots, express f(x) as f(-x).
The no. of sign changes from the term with highest degree of x to that with lowest degree of x is 4. Thus max. possible no. of negative roots is 4.
