You use the discriminant of the quadratic formula which is [tex] \sqrt{b^{2} - 4ac} [/tex] Using the values of the given quadratic formula you will find that [tex]d = \sqrt{4} [/tex] If the discriminant equals less than 0 you have no real roots(imaginary roots). If it equals exactly 0, you have 2 real equal roots. If it is more than 0, then you have two different real roots.
Therefore the quadratic function [tex] {4x}^{2} + 6x + 2[/tex] Will have two real roots.
