Question

Is there a way to simplify the process of plugging in factors through synthetic division to find the zeros of a polynomial? I am aware of Descarte's Rule of Signs, but is there any other way to make it faster than guess-and-check?

Answer 1

Yes you can use the discriminant of a quadratic/polynomial. For instance, if

`b^2 - 4ac = 0` there is one real root. If
`b^2 - 4ac > 0` there are two real roots and i
`b^2 - 4ac < 0` there are no real roots

The discriminant comes from the quadratic equation, which is the following.

`<span>x = (-b \pm √(b^2-4ac))/(2a)</span>`