Quadratic Equations — Formula Sheet

ax²+bx+c=0, a≠0

aα²+bα+c=0

If a·b=0, then a=0 or b=0 or both

(x+b/2a)²=(b²-4ac)/4a²

(2ax+b)²=b²-4ac

x=(-b±√D)/2a

For x²-18x+72=0, x=6 is verified as a root by substitution.

Quadratic equation

ax^2+bx+c=0, a not equal to zero

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