Answer:To find the roots of the quadratic equation x^2 + 4x + 3 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the following formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 4, and c = 3. Substituting these values into the formula, we get:
x = (-4 ± √(4^2 - 4(1)(3))) / (2(1))
Simplifying further:
x = (-4 ± √(16 - 12)) / 2
x = (-4 ± √4) / 2
Now, we can simplify the square root:
x = (-4 ± 2) / 2
This gives us two possible solutions:
x = (-4 + 2) / 2 = -2/2 = -1
x = (-4 - 2) / 2 = -6/2 = -3
Therefore, the roots of the equation x^2 + 4x + 3 = 0 are x = -1 and x = -3.
Explanation: