Roots and factors are important parts of quadratic equations.

A quadratic equation usually looks like this:

$ax^2 + bx + c = 0$

Here, the "roots" are the values of $x$ that make this equation true. They are also the spots where the graph touches or crosses the x-axis.

Now, let’s talk about factors. We can write the quadratic expression in a different way:

$a(x - r_1)(x - r_2)$

In this expression, $r_1$ and $r_2$ are the roots we just mentioned.

Example

Let's look at the quadratic $2x^2 - 8x + 6$. We can find its roots using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

To find the roots, we do these steps:

1. Find the roots:

   • We have $b = -8$, $a = 2$, and $c = 6$.
   • This gives us the roots $r_1 = 1$ and $r_2 = 3$.

2. Write it in factor form:

   • So, we can write it as $2(x - 1)(x - 3)$.

This link between roots and factors is really important for solving and understanding quadratic equations.