Question

Solve the polynomial equation by finding all roots,

125x^3-8=0
A) x = 2/5, x = -1/5, x = -1/5
B) x = 2, x = -2/5, x = 2/5
C) x = 2/5, x = -2/5, x = -2/5
D) x = 2/5, x = -2/5, x = 1/5

Answer 1

To solve the equation 125x^3-8=0, we can rearrange it to the form ax^3+b=0 and use the formula for the roots of a quadratic equation.

Step-by-step explanation:

To solve the equation 125x^3-8=0, we can rearrange it to the form ax^3+b=0. In this case, a=125 and b=-8. The roots can be found using the formula for the roots of a quadratic equation, which is x = (-b/a)^(1/3). By substituting the values for a and b, we get:

x = (-(-8)/125)^(1/3) = 2/5

Therefore, the correct answer is D) x = 2/5, x = -2/5, x = 1/5.