Final answer:
The question pertains to selecting the correct solution for the variable X from a given augmented matrix. Solving such a matrix typically involves obtaining the row-echelon form and then performing back-substitution. The use of the quadratic formula is indicated, but without seeing the matrix, choosing the correct solution for X from the options is not possible.
Step-by-step explanation:
The student has been presented with a system of equations and an augmented matrix leading to solution options for the variable X. Without the specific matrix or its row-echelon form, it's not possible to confirm which of the provided solutions is correct. However, the student's question seems related to solving a system of linear equations, which typically involves manipulating the matrix into row-echelon form and then performing back-substitution to find the values of the variables. If the system is in one variable, the row-echelon form will directly provide the value of X. Given that several example equations in the form ax² + bx + c = 0 are provided, these can be solved using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). The examples given apply this formula and find positive and negative roots, but without the context of the matrix, it's not possible to confirm which solution for X is correct.