# How do you find the roots, real and imaginary, of y=(x/5-1)(-3x+5) using the quadratic formula?

Feb 15, 2016

roots are $x = 5$, and $x = \frac{5}{3}$; both real.

#### Explanation:

Given equation

$y = \left(\frac{x}{5} - 1\right) \left(- 3 x + 5\right)$
As factors of the quadratic have already been given, there is no need to use the quadratic formula.

The roots can be obtained by setting each of the factors equal to zero separately.
$\therefore$ either the factor $\left(\frac{x}{5} - 1\right) = 0$, or factor$\left(- 3 x + 5\right) = 0$
$\left(\frac{x}{5} - 1\right) = 0$ gives us $x = 5$
and $\left(- 3 x + 5\right) = 0$ gives us $x = \frac{5}{3}$