Let's solve the provided polynomial equation step-by-step. We'll make sure to identify the correct polynomial expression and solve it accordingly.
First, we need to recognize and arrange the given polynomial equation in its standard form. It looks like the given polynomial has some formatting issues. We’ll consider the corrected form based on the solution provided.
Based on the solution given, we have the following polynomial equation of degree 6:
[tex]\[ P(x) = x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2 = 0 \][/tex]
This is a sixth-degree polynomial, meaning it can have up to 6 real or complex roots.
To solve a polynomial equation, we will identify its coefficients and arrange it in polynomial form:
[tex]\[ x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2 = 0 \][/tex]
The solutions to this polynomial equation are given by finding the values of [tex]\( x \)[/tex] that satisfy it. In our case, the results from solving this polynomial equation provide six roots, generally represented in the form of CRootOf (Complex Root Of).
The roots of the polynomial equation [tex]\( P(x) = 0 \)[/tex] are:
[tex]\[ x_1 = \text{CRootOf}(x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2, 0) \][/tex]
[tex]\[ x_2 = \text{CRootOf}(x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2, 1) \][/tex]
[tex]\[ x_3 = \text{CRootOf}(x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2, 2) \][/tex]
[tex]\[ x_4 = \text{CRootOf}(x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2, 3) \][/tex]
[tex]\[ x_5 = \text{CRootOf}(x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2, 4) \][/tex]
[tex]\[ x_6 = \text{CRootOf}(x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2, 5) \][/tex]
Each [tex]\( \text{CRootOf} \)[/tex] notation represents a root of the given polynomial, uniquely identifying one of the six roots.
Therefore, the solutions to the polynomial equation [tex]\( x^6 + 60x^5 - 57x^4 + 6x^3 - x^2 + 6x + 2 = 0 \)[/tex] are the six roots listed above.
