Answer:
The solutions are a₁ = -4/19 i, a₂ = 4/19 i and a₃ = -1/4
Step-by-step explanation:
Given the equation 76a³+19a²+16a=-4, for us to solve the equation, we need to find all the factors of the polynomial function. Since the highest degree of the polynomial is 3, the polynomial will have 3 roots.
The equation can also be written as (76a³+19a²)+(16a+4) = 0
On factorizing out the common terms from each parenthesis, we will have;
19a²(4a+1)+4(4a+1) = 0
(19a²+4)(4a+1) = 0
19a²+4 = 0 and 4a+1 = 0
From the first equation;
19a²+4 = 0
19a² = -4
a² = -4/19
a = ±√-4/19
a₁ = -4/19 i, a₂ = 4/19 i (√-1 = i)
From the second equation 4a+1 = 0
4a = -1
a₃ = -1/4
