To solve the quadratic equation 3x2 + 42x + 3 = 0, we can either use the quadratic formula or factorization. In this case, it may be easier to apply the quadratic formula, which is:
x = (-b ± √(b² – 4ac)) / (2a)
For the equation given:
- a = 3
- b = 42
- c = 3
Now, we can plug these values into the formula:
1. Calculate the discriminant:
b² – 4ac = 42² – 4 * 3 * 3
This simplifies to:
1764 – 36 = 1728
2. Since the discriminant is positive, we have two real solutions:
x = (-42 ± √1728) / (2 * 3)
Calculating the square root of 1728 gives us:
√1728 ≈ 41.57
This leads to the two potential solutions:
x₁ = (-42 + 41.57) / 6 ≈ -0.0717
x₂ = (-42 – 41.57) / 6 ≈ -13.595
Now, we have two solutions: x ≈ -0.0717 and x ≈ -13.595. Next, let’s check if any of the values given in the original question (4, 3, 3, 2, 4) are solutions:
None of the values 4, 3, 2 match our calculated solutions, which indicates that the given options do not solve the equation. Therefore, the final conclusion is:
No valid solutions among the options provided.