Final answer:
Using the quadratic formula with coefficients a=1, b=5, and c=3 from the quadratic equation x^2 + 5x + 3 = 0, we find that the roots are x equals the quantity of negative 5 plus or minus square root 13 all over 2.
Step-by-step explanation:
To solve the quadratic equation x^2 + 5x + 3 = 0, we can use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) where a, b, and c are coefficients from the equation ax^2 + bx + c = 0.
In this case, a = 1, b = 5, and c = 3. Plugging these values into the formula gives us:
x = (-(5) ± √((5)^2 - 4(1)(3)) / (2(1))
x = (-5 ± √(25 - 12)) / 2
x = (-5 ± √(13)) / 2
Therefore, the correct answer is:
x equals the quantity of negative 5 plus or minus square root 13 all over 2.