# Find the quadratic equation, whose roots are 5 and -4 and leading coefficient is 3?

Apr 1, 2017

$3 {x}^{2} - 3 x - 60 = 0$

#### Explanation:

A quadratic equation whose roots are $\alpha$ and $\beta$ and leading coefficient is $a$ is

$a \left(x - \alpha\right) \left(x - \beta\right) = 0$

Hence, the quadratic equation whose roots are $5$ and $- 4$ and leading coefficient is $3$ is

$3 \left(x - 5\right) \left(x - \left(- 4\right)\right) = 0$

or $3 \left(x - 5\right) \left(x + 4\right) = 0$

or $3 \left({x}^{2} - 5 x + 4 x - 20\right) = 0$

or $3 \left({x}^{2} - x - 20\right) = 0$

or $3 {x}^{2} - 3 x - 60 = 0$