To solve the equation a2 + 3a + 8 = 0, we can use the quadratic formula, which is a = (-b ± √(b² – 4ac)) / 2a. Here, the coefficients are:
- a (the coefficient of a2): 1
- b (the coefficient of a): 3
- c (the constant term): 8
Plugging in these values into the quadratic formula:
a = ( -3 ± √(3² – 4 * 1 * 8) ) / (2 * 1)
Calculating the discriminant:
3² = 9 and 4 * 1 * 8 = 32, so:
9 – 32 = -23
Since the discriminant is negative, this means the equation has no real solutions. Instead, it has two complex solutions.
Thus, the final answers can be expressed as:
a = (-3 ± √(-23)i) / 2
So the value of a can be expressed in terms of complex numbers.