Math Problem Statement

Find all zeros of the function f(x)=2x^3 - 4x^2 + 100. Enter the zeros separated by commas.just give answer

Solution

The zeros of the function f(x)=2x3−4x2+100f(x) = 2x^3 - 4x^2 + 100 are:

x≈3.5665,−0.5665x \approx 3.5665, -0.5665 (two real zeros).

The third zero is a complex number:

x=−i⋅5x = -i \cdot 5.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Equations
Complex Numbers

Formulas

Cubic equation formula ax^3 + bx^2 + cx + d = 0
Quadratic formula for solving the reduced polynomial

Theorems

Fundamental Theorem of Algebra
Cardano's Method for solving cubic equations

Suitable Grade Level

Grades 10-12

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