Hello!
In math, there is always something called the discriminant. This is represented by the equation [tex]b^{2} -4ac[/tex], when a quadratic = [tex]ax^{2} + bx + c[/tex]. The discriminant tells you what roots an equation has. A discriminant of over 0 represents 2 real roots, a discriminant of 0 = 1 real root, and a discriminant of <0 is 0 real roots (2 complex roots)
Now, substitute in the values and solve. In this equation, a = 5, b = 2, c = 1.
[tex]b^{2} -4ac[/tex]
[tex]2^{2} -4(5)(1)[/tex]
[tex]4 - 20[/tex]
[tex]-16[/tex]
Therefore, the discriminant is -16. This means that the equation has no real roots, and has 2 complex roots. Therefore, your answer is D.
Hope this helps!
