Question

Let f(x) = -2x^3 + 8x.
a. Find the real zeros of f.

Answer 1

To find the real zeros of the function f(x) = -2x^3 + 8x, factor out x and solve for the remaining quadratic equation using the quadratic formula.

Step-by-step explanation:

To find the real zeros of the function f(x) = -2x^3 + 8x, we set f(x) equal to zero and solve for x.

-2x^3 + 8x = 0

Factor out x: x(-2x^2 + 8) = 0

Set each factor equal to zero: x = 0 and -2x^2 + 8 = 0

Solve the second equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = -2, b = 0, and c = 8. Substituting these values, we get:

x = (-0 ± √(0^2 - 4(-2)(8))) / (2(-2))

x = (± √(64)) / (-4)

Therefore, the real zeros of f(x) are x = 0, x = -2, and x = 2.