Question

How to find zeros of cubic polynomial?

Answer 1

Find the zeros of cubic polynomial :

A cubic polynomial is of the form $a{x}^3+b{x}^2+cx+d$

If $\alpha ,\beta ,\gamma$ are the zeros of cubic the polynomial then it satisfy the following condition

1. $\alpha +\beta +\gamma =-\frac{b}{a}$
2. $\alpha \beta +\beta \gamma +\alpha \gamma =\frac{c}{a}$
3. $\alpha \beta \gamma =-\frac{d}{a}$

Solving this equations we can get the zeros of the cubic polynomial.

Zeros of a polynomial is defined as the point at which the polynomial become zero. The degree of a polynomial is the highest power of the variable $x$. A cubic polynomial will invariably have at least one real zero. The following cases are possible fore the zeros of a cubic polynomial.

1. All three zeros might be real and distinct.
2. All three might be real and two of them might be equal.
3. All zeros might be real and equal
4. One zero might be real and other two are complex

Hence, by satisfying the equations of zeroes, we can get the zeros of the cubic polynomial.