How many zeros are there in the function f (x) = 7x13 - 12x9 + 16x5 - 23x + 42?

We will use the Descartes' rule of signs and see how many times the signs change from positive to negative and from negative to positive from one term to the next (two consecutive terms are with different signs).

In this case it is 4 times (+7x13 to - 12x9, - 12x9 to + 16x5, + 6x5 to - 23 x and finally - 23x to + 42).

Answer: There are 4 real zeroes.