Questions: Use ZERO (or ROOT) to approximate the positive x-intercept(s) of the equation. y=x^4-3.8x^3-35.99x^2+75.24x+392.04

Solution Steps

To approximate the positive x-intercept(s) of the given polynomial equation, we can use numerical methods such as the Newton-Raphson method or the bisection method. In Python, we can utilize libraries like scipy.optimize to find the roots of the polynomial.

We are given the polynomial equation:

\[ y = x^{4} - 3.8 x^{3} - 35.99 x^{2} + 75.24 x + 392.04 \]

To find the positive x-intercept, we need to solve for \( x \) when \( y = 0 \). Using numerical methods, we approximate the root of the equation. The initial guess for the root is set to \( x = 5 \).

After applying the numerical method, we find that the positive x-intercept is approximately:

\[ x \approx 5.5000 \]

Final Answer