The solutions of the quadratic equation x² + 7x + 4 can be found using the quadratic formula:
x = (-b ± √(b² – 4ac)) / (2a)
For our equation, we have:
- a = 1
- b = 7
- c = 4
Now, we plug in these values into the formula:
1. Calculate the discriminant (b² – 4ac):
Discriminant = 7² – 4(1)(4) = 49 – 16 = 33
2. Since the discriminant is positive, we have two distinct real solutions:
x = (-7 + √33) / 2 and x = (-7 – √33) / 2
3. Therefore, the roots or solutions of the equation are:
x ≈ -1.5 (when using the positive root) and x ≈ -5.5 (when using the negative root).
In conclusion, the quadratic equation x² + 7x + 4 has two real solutions, which can be expressed more precisely as:
x = -7/2 + √33/2 and x = -7/2 – √33/2.