# How do you find the number of complex, real and rational roots of 2x^2+5x+3=0?

Sep 17, 2016

There are two rational roots $: - 1 , - \frac{3}{2}$.

#### Explanation:

$2 {x}^{2} + 5 x + 3 = 0$

$\therefore \underline{2 {x}^{2} + 2 x} + \underline{3 x + 3} = 0$

$\therefore 2 x \left(x + 1\right) + 3 \left(x + 1\right) = 0$

$\therefore \left(x + 1\right) \left(2 x + 3\right) = 0$

$\therefore x = - 1 , \mathmr{and} , x = - \frac{3}{2}$

Thus, there are two rational roots $: - 1 , - \frac{3}{2}$.