Final answer:
The zeros of the equation -x⁵ + 4x⁴ + 24x³ - 96x² + 25x = 100 are approximately 0.0145 and -1.462.
Step-by-step explanation:
The equation -x⁵ + 4x⁴ + 24x³ - 96x² + 25x = 100 can be rearranged as x² + 0.0211x - 0.0211 = 0. To solve for the zeros, we can use the quadratic formula. The formula is x = (-b ± sqrt(b² - 4ac)) / (2a). In this case, a = 1, b = 0.0211, and c = -0.0211. Plugging in these values, we get x = (-0.0211 ± sqrt(0.0211² - 4(1)(-0.0211))) / (2(1)). Simplifying the equation, we find x ≈ 0.0145 and x ≈ -1.462.