Questions: Use the numerical solver on your graphing calculator to solve the equation for all real solutions. Enter your answer as a list of numbers separated with commas: Example: -4,3,2.5 x^3-1.8x^2-18.79x+17.64=0 Solutions = Make sure your answers are accurate to at least two decimals

Solution Steps

To solve the given cubic equation for all real solutions, we can use a numerical solver to find the roots. In Python, we can utilize the numpy library's roots function, which computes the roots of a polynomial with given coefficients. We will then filter out the real roots and round them to two decimal places for accuracy.

We are given the cubic polynomial equation:

\[ x^{3} - 1.8x^{2} - 18.79x + 17.64 = 0 \]

Using numerical methods, we find the roots of the polynomial. The roots are:

\[ 4.9, -4.0, 0.9 \]

The roots are already expressed to two decimal places, so we retain them as:

\[ 4.9, -4.0, 0.9 \]

Final Answer