Question

Solve the eqauation 76a^3+19a^2+16a=-4

Answer 1

To solve the equation 76a^3 + 19a^2 + 16a = -4, we can use the quadratic formula to find the solutions.

Step-by-step explanation:

To solve the equation 76a^3 + 19a^2 + 16a = -4, we can rearrange the equation to form a quadratic equation in the form ax^2 + bx + c = 0. In this case, the constants are a = 76, b = 19, and c = -4. We can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

We substitute the values of a, b, and c into the formula and solve for x:

x = (-19 ± √(19^2 - 4*76*(-4))) / (2*76)

After evaluating the expression inside the square root, we find that the solutions to the equation are:

x = -1/4, -1/19, and -4/19

Answer 2

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