Question

3x square + x+ 1 = 0 nature roots

Answer 1

Expression : $\underline{ \boxed{3 {x}^{2} + x + 1 = 0}}$

This is of the form : $\underline{ \boxed{a {x}^{2} + bx + c = 0}}$

Now,
Discriminant,
$\bf D = {b}^{2} - 4ac \\ \\ \quad = {(1)}^{2} - 4(3)(1) \\ \\ \quad = 1 - 12 \\ \\ \quad = - 11$

Here,
$\bf \: D < 0$

Hence, the nature of roots are as follows :

⚪The roots are imaginary

⚪The roots are complex