# How do you write a quadratic equation in standard form with the given root(s) 3, 2/5?

Sep 5, 2016

$5 {x}^{2} - 17 x + 6 = 0$

#### Explanation:

If the roots of an equation are $a$ and $b$, the equation would be

$p \left(x - a\right) \left(x - b\right) = 0$, where $p$ is any constant

As roots are $3$ and $\frac{2}{5}$ the equation is

$\left(x - 3\right) \left(x - \frac{2}{5}\right) = 0$ i.e.

${x}^{2} - \frac{2}{5} x - 3 x + \frac{6}{5} = 0$ or

${x}^{2} - \frac{17}{5} x + \frac{6}{5} = 0$ or

$5 {x}^{2} - 17 x + 6 = 0$