Question
What are the zeros of the function?
f(x) = x^3 +6x^2 + 8x
f(x) = x^3 +6x^2 + 8x
Answers
Answered by
GPT 3.5
To find the zeros of the function, we need to solve the equation f(x) = x^3 + 6x^2 + 8x = 0.
We can factor out an x from the equation to get:
x(x^2 + 6x + 8) = 0
Now, we can solve for x by setting each factor equal to zero:
x = 0
x^2 + 6x + 8 = 0
To solve the quadratic equation x^2 + 6x + 8 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 6, and c = 8. Plugging in these values, we get:
x = (-6 ± √(6^2 - 4(1)(8))) / (2(1))
x = (-6 ± √(36 - 32)) / 2
x = (-6 ± √4) / 2
x = (-6 ± 2) / 2
This gives two possible solutions:
x1 = (-6 + 2) / 2 = -4 / 2 = -2
x2 = (-6 - 2) / 2 = -8 / 2 = -4
Therefore, the zeros of the function f(x) = x^3 + 6x^2 + 8x are x = 0, x = -2, and x = -4.
We can factor out an x from the equation to get:
x(x^2 + 6x + 8) = 0
Now, we can solve for x by setting each factor equal to zero:
x = 0
x^2 + 6x + 8 = 0
To solve the quadratic equation x^2 + 6x + 8 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 6, and c = 8. Plugging in these values, we get:
x = (-6 ± √(6^2 - 4(1)(8))) / (2(1))
x = (-6 ± √(36 - 32)) / 2
x = (-6 ± √4) / 2
x = (-6 ± 2) / 2
This gives two possible solutions:
x1 = (-6 + 2) / 2 = -4 / 2 = -2
x2 = (-6 - 2) / 2 = -8 / 2 = -4
Therefore, the zeros of the function f(x) = x^3 + 6x^2 + 8x are x = 0, x = -2, and x = -4.