Zeroes of a Polynomial

Definition

The zeros of a polynomial $f(x)$are the values of $x$ which satisfy the equation $f(x)=0$. Here $f(x)$ is a function of $x$, and the zeros of the polynomial are the values of $x$ for which the $f(x)$ value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation $f(x)=0$. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.

How to Find Zero of a Polynomial?

Linear Equation

A linear equation is of the form $y=ax+b$. The zero of this equation can be calculated by substituting $y=0$, and on simplification we have $ax+b=0$ or $x=-{\frac {b}{a}}$.

Quadratic Equation

The quadratic equation of the form $x^{2}+x(a+b)+ab=0$ can be factorized as $(x+a)(x+b)=0$, and we have $x=-a$ or $x=-b$ as the zeros of the polynomial. And for a quadratic equation of the form $ax^{2}+bx+c=0$ which cannot be factorized, the zeros can be calculated using the formula $x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}$