The solutions are not displayed properly, therefore, I cannot provide an exact answer.
However, I will help you get the solutions for each of the given equations and then you can pick your correct one.
The general form of the quadratic equation is:
ax² + bx + c = 0
The solutions of a quadratic equation can be calculated using the quadratic formula shown in the attached image.
For the first choice:
2x² + 6x + 9 = 0
comparing this equation with the general formula, we will find that:
a = 2
b = 6
c = 9
Substituting with the values of a,b and c in the quadratic formula, we will find that that the solutions of this equation are [tex]- \frac{3}{2} + \frac{3i}{2} [/tex] and [tex]- \frac{3}{2} - \frac{3i}{2} [/tex]
For the second choice:
x² + 3x + 12 = 0
comparing this equation with the general formula, we will find that:
a = 1
b = 3
c = 12
Substituting with the values of a,b and c in the quadratic formula, we will find that that the solutions of this equation are [tex]- \frac{3}{2} + \frac{ \sqrt{39}i}{2} [/tex] and [tex]- \frac{3}{2} - \frac{ \sqrt{39}i}{2} [/tex]
For the third choice:
x² + 3x + 3 = 0
comparing this equation with the general formula, we will find that:
a = 1
b = 3
c = 3
Substituting with the values of a,b and c in the quadratic formula, we will find that that the solutions of this equation are [tex]- \frac{3}{2} + \frac{ \sqrt{3} i}{2} [/tex] and [tex]- \frac{3}{2} - \frac{ \sqrt{3} i}{2} [/tex]
For the fourth choice:
2x² + 6x + 3 = 0
comparing this equation with the general formula, we will find that:
a = 2
b = 6
c = 3
Substituting with the values of a,b and c in the quadratic formula, we will find that that the solutions of this equation are [tex] \frac{-3+ \sqrt{3} }{2} [/tex] and [tex] \frac{-3- \sqrt{3} }{2} [/tex]
Hope this helps :)
