Respuesta :
We must solve for x the following equation: "zero equals X squared minus 7X -18", mathematically this equation is:
[tex]0=X^2-7X-18.[/tex]Solving this equation is equivalent to find the roots of a polynomial of degree 2. A polynomial of degree 2 always has 2 roots, and they are given by the following equations:
[tex]\begin{gathered} x_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a}, \\ x_2=\frac{-b-\sqrt[]{b^2-4ac}}{2a}, \end{gathered}[/tex]where the coefficients a, b and c are coefficients of each term of the polynomial:
[tex]aX^2+bX+c\text{.}[/tex]Comparing with the polynomial of the problem, we see that the coefficients are:
[tex]a=1,b=-7,c=-18.[/tex]Replacing the values of the coefficients in the formulas for the roots above, and computing, we get:
[tex]\begin{gathered} x_1=\frac{-(-7)+\sqrt[]{(-7)^2-4\cdot1\cdot(-18)}}{2\cdot1}=9, \\ x_2=\frac{-(-7)-\sqrt[]{(-7)^2-4\cdot1\cdot(-18)}}{2\cdot1}=-2, \end{gathered}[/tex]Answer
The solutions to the equation of the problem are:
[tex]\begin{gathered} x_1=9, \\ x_2=-2. \end{gathered}[/tex]