Quadratic Equations

A polynomial of second degree

A polynomial of second degree is called a quadratic polynomial. It has the form $ax^2+bx+c$, where $a,b,c$ are real numbers and $a\neq 0$. Examples in

A polynomial of first degree

A polynomial of first degree is called a linear polynomial. It has the form $ax+b$, where $a,b$ are real numbers and $a\neq 0$.

An equation of the form $ax^2+bx+c=0$

An equation of the form $ax^2+bx+c=0$, with $a\neq 0$, is called a quadratic equation in one variable $x$.

A real number $\alpha$ is

A real number $\alpha$ is a root of $ax^2+bx+c=0$ if and only if it satisfies the equation, that is, $a\alpha^2+b\alpha+c=0$.

If $a\cdot b=0$

If $a\cdot b=0$, then $a=0$ or $b=0$ or both are zero.