Examine the variations in sign for and .

If is a polynomial function with real coefficients then,

(a).

The number of positive real zeros of is equal to the number of variations in sign of or less than that number by some even number

(b).

The number of negative real zeros of is same as the number of variations in sign of

or less than that number by some even number.

The function is .

Consider .

has variations in sign.

has variations in sign.

Therefore by Descartes rule of signs has either or positive real zeros and  

negative zero.

has either or positive real zeros and negative zero.