Answer:
No real roots
Step-by-step explanation:
The given quadratic equation is
[tex] {x}^{2} + 5x + 7 = 0[/tex]
Comparing this to the general quadratic equation:
[tex]a {x}^{2} + bx + c = 0[/tex]
We have a=1, b=5 and c=7
Recall that the discriminant is
[tex]D = {b}^{2} - 4ac[/tex]
We plug in the values to get:
[tex]D = {5}^{2} - 4(1)(7)[/tex]
[tex]D =25- 28 = - 3[/tex]
Since the discriminant is less than zero, the given equation has no real roots
