f(x) = -x^3 +5x+2

estimate solutions with f(x)=-4

The approximate solutions for the equation \( -x^3 + 5x + 6 = 0 \) are:

\[
x_1 \approx -1.29, \quad x_2 \approx 2.69
\]

These values are the estimates for the roots where \( f(x) = -4 \). The function crosses the x-axis near these points.

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Here are 5 related questions you might explore:
1. How do we exactly find the roots of a cubic equation?
2. What is the behavior of cubic functions as \(x\) approaches infinity?
3. How can we verify if a value is an exact solution for a cubic equation?
4. What methods exist to find the roots of higher-degree polynomials?
5. How does graphing help estimate the solutions of equations?

**Tip**: Checking solutions by substitution can help verify the accuracy of the approximations.

f(x) = -x^3 +5x+2. Estimate solutions with f(x)=-4.

Discover how to estimate the roots of the cubic equation -x^3 + 5x + 2 where f(x) = -4. Learn about key algebraic concepts, including root approximation methods, and the Intermediate Value Theorem. Suitable for Grades 10-12.

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