C
1) Let's complete the square for this quadratic equation g² +6g +4 = 0
g² +6g +4 = 0 Divide the coefficient b by 2: 6/2 = 3
Subtract 4 from both sides
g² +6g = -4 Add 9 to both sides
g² +6g +9 = -4 + 9 Rewrite it as a binomial (a+b)²
(g+3)² = 5 Take the square root on both sides
√(g+3)² = √5
g+3 =+√5, -√5 Subtract 3 from both sides
g = -3 +√5, -3 -√5
2) Hence, the roots for this quadratic equation are:
[tex]S=\mleft\lbrace-3+\sqrt[]{5},\text{ 3-}\sqrt[]{5}\mright\rbrace[/tex]3) Hence, the answer is C
