The Sum and Product of Roots Theorem

From the quadratic formula, we know that the numbers $latex r_1$ and $latex r_2$ are the roots of the quadratic equation $latex ax^2 + bx +c =0$ where $latex a \neq 0$ if and only if

$latex r_1 + r_2 = -\frac{b}{a}$

and

$latex r_1r_2 = \frac{c}{a}$.  Continue reading

The Quadratic Formula Theorem

Introduction

The quadratic formula is a formula in getting the roots of the quadratic equation $latex ax^2 + bx + c = 0$, where $latex a$, $latex b$ and $latex c$ are real numbers and $latex a \neq 0$. The quadratic formula is a generalization of completing the square, and it is usually used as a calculation strategy if a quadratic equation is not factorable.

In the graph of the quadratic function $latex f(x) = ax^2 + bx + c$, the values of $latex x$ in $latex ax^2 + bx + c = 0$, are the coordinates of $latex x$ where the curve pass through.

But how did mathematicians come up with the quadratic formula? How were they able to invent such complicated formula? In this post, we discuss the derivation of the quadratic formula. Continue reading