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 ).
There are 4 real zeroes.