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.
