# How do you write a quadratic equation in standard form with the given roots 1/4, 3?

Jun 9, 2017

$4 {x}^{2} - 13 x + 3 = 0$

#### Explanation:

For a quadratic equation of the form: $a {x}^{2} + b x + c = 0$ to have roots of $\frac{1}{4}$ and $3$

$\to \left(4 x - 1\right) \mathmr{and} \left(x - 3\right)$ must be factors of $a {x}^{2} + b x + c$

$\therefore \left(4 x - 1\right) \left(x - 3\right) = 0$

$4 {x}^{2} - 13 x + 3 = 0$

$a = 4 , b = - 13 , c = 3$