Find the zeros of I(x)=12x^3/5-27x/5

1 answer

To find the zeros of the function I(x) = (12x^3/5) - (27x/5), we need to set the function equal to zero and solve for x.

12x^3/5 - 27x/5 = 0

Multiply both sides of the equation by 5 to remove the denominators:

12x^3 - 27x = 0

Factor out the common term x:

x(12x^2 - 27) = 0

Set each factor equal to zero:

x = 0

12x^2 - 27 = 0

To solve the quadratic equation, we can factor it further:

12x^2 - 27 = 0

3(4x^2 - 9) = 0

3(2x - 3)(2x + 3) = 0

Setting each factor equal to zero:

2x - 3 = 0 or 2x + 3 = 0

Solving each equation separately:

2x - 3 = 0 --> 2x = 3 --> x = 3/2

2x + 3 = 0 --> 2x = -3 --> x = -3/2

Therefore, the zeros of the function I(x) = (12x^3/5) - (27x/5) are x = 0, x = 3/2, and x = -3/2.