Question

Solve the equations using the Quadratic Formula.

x² + 3x + 1 = 0
A) x = -2, x = -1
B) x = -1, x = 2
C) x = -3, x = 1
D) x = 1, x = -4

Answer 1

The quadratic equation x² + 3x + 1 = 0 can be solved using the Quadratic Formula, which results in two solutions. However, the solutions are not integers, meaning none of the provided options A, B, C, or D are correct.

Step-by-step explanation:

To solve the quadratic equation x² + 3x + 1 = 0 using the Quadratic Formula, we identify the coefficients of the equation which are: a=1, b=3, and c=1.

The Quadratic Formula is given by x = (-b ± √(b²-4ac)) / (2a). Plugging in the values we have:

x = (-(3) ± √((3)²-4(1)(1))) / (2(1))

x = (-3 ± √(9-4)) / 2

x = (-3 ± √(5)) / 2

Therefore, the solutions for x are:

• x = (-3 + √5) / 2
• x = (-3 - √5) / 2

Since none of our solutions are integers, we conclude that the options A, B, C, and D are incorrect.