Finding roots of polynomials, negative square root The formula for finding the roots of a polynomial is as follows
$$x = \frac {-b \pm \sqrt{ b^2 - 4ac }}{2a} $$

what happens if you want to find the roots of a polynomial like this simplified one

$$ 3x^2 + x + 24 = 0 $$

then the square root value becomes

$$ \sqrt{ 1^2 - 4\cdot3\cdot24 } $$


$$ = \sqrt{ -287 } $$
which is the square root of a negative number, which isn't allowed. What do you do in this case? I know there are other methods, i.e. factorisation and completing the square, but does this mean that this formula can only be used in specialised cases or have i gone wrong somewhere along the path?

Yeah so have you read about complex numbers. The root will be 
$$x = \frac{-1 \pm{i} \sqrt{287}}{2 \times 3}$$

where $i=\sqrt{-1}$. Read more about complex numbers and when a polynomial can have complex roots, that happens when the *Discriminant* factor $b^{2}-4ac <0$. 
