what is the root of the polynomial equation ( x(x - 2)(x + 3)=18 )? use a graphing calculator and a system…
what is the root of the polynomial equation ( x(x - 2)(x + 3)=18 )? use a graphing calculator and a system of equations.
Answer
Explanation:
Step1: Set up the system of equations
Let (y_1=x(x - 2)(x + 3)=x^{3}+x^{2}-6x) and (y_2 = 18)
Step2: Graph the two equations
Using a graphing calculator, graph (y=x^{3}+x^{2}-6x) and (y = 18)
Step3: Find the intersection point
The (x) - coordinate of the intersection point of the two graphs is the root of the equation (x(x - 2)(x + 3)=18)
When (x = 3): [ \begin{align*} y_1&=3\times(3 - 2)\times(3+ 3)\ &=3\times1\times6\ &=18=y_2 \end{align*} ]
Answer:
(3)