# What does Descartes' rule of signs tell you about the real roots of the polynomial?

Real roots of the polynomial mean zeros of the polynomial in real numbers.

## Answer: We use Descartes' rule of signs to determine the number of positive real roots or negative real roots for the given polynomial function.

Let us understand Descartes' rule of signs.

**Explanation:**

Let f(x) be a polynomial function. Descartes's rule of signs states the following:

- The number of positive real roots is either equal to change in the sign of coefficients of (x) or less than it by an even number.
- The number of negative real roots is either equal to change in the sign of coefficients of f(-x) or less than it by an even number.

Let us understand this by example. Consider f(x) = x^{5} + 4x^{4} - x^{3} + 2x^{2} - 9

Observe that there is a 3 times change in the signs of coefficient in this polynomial function. So, this function f(x) has either 3 or 1 positive real roots.

Now, f(-x) = - x^{5} + 4x^{4} + x^{3} + 2x^{2} - 9

Here, there is a 2 times change in the signs of coefficient in f(-x). So, this function f(x) has either 2 or 0 negative real roots.