In this section we learn how to solve quadratic equations.
By the end of this section, we'll know how to solve equations like:
\[6x^2-x-2 = 0\]
We start by watching the tutorial, below. We then read through a summary of the two-step method for solving quadratic equations that we see in the tutorial. Finally we work through some questions each of which has both an answer key and video detailed solutions.
The following tutorial covers all of the essentials we'll need to know about the quadratic formula.
It lasts a little more than \(10\) minutes, do take notes! This should help you understand/know how to use the quadratic formula.
Given a quadratic equation: \[ax^2+bx+c = 0\] we can solve this equation for \(x\) using the following two steps:
Using the quadratic formula, solve each of the following for \(x\):
Solution(s) to quadratic equations won't always be "nice" round numbers.
For example, we'll be seeing below, the quadratic equation: \[-3x^2+5x-1 = 0\] Has solutions: \[x = \frac{5+\sqrt{13}}{6} \quad \text{and} \quad x = \frac{5-\sqrt{13}}{6}\] We'll be faced with this type of solution, in which the \(x\) values are irrational numbers, as soon as the discriminant \(\Delta \) isn't a square number (the square root therefore cannot be simplified).
Solve each of the following for \(x\).
Write your answers in irrational form and (using your calculator) write their values rounded to three significant figures.