Solving Polynomial Equations using Technology

Question 1

Explain why the graphing calculator cannot be used to solve or approximate solutions to all polynomial equations.

Revolt · Accepted Answer

A graphing calculator can only find real solutions to polynomial equations because it relies on identifying x-intercepts or points of intersection on the Cartesian (x-y) plane. However, some polynomial equations have complex solutions. Because the x-axis only represents real numbers, complex solutions do not appear as x-intercepts, and a system with only complex solutions will not intersect on a standard graph. Therefore, the graphing calculator cannot be used to solve for or approximate these non-real roots.

Question 2

Sun shades are sold in the shape of right isosceles triangles. If the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade?

Revolt · Accepted Answer

and

Question 3

-5.7 or 5.7-8 or 8✔ -11.3 or 11.3-32 or 32

Revolt · Accepted Answer

✔ -11.3 or 11.3; Use the graphing calculator to graph the system. The solutions to the system are . Since the side lengths of a triangle must be positive, the length of one leg of the sun shade is feet.: -11.3 or 11.3

Question 4

Select any of the following you included in your explanation.

Revolt · Accepted Answer

Graphing the related system means that you do not have to rewrite the equation to set it equal to 0. It is easier because you can just graph each side of the equation.; Sometimes it is difficult to locate the intersection point for the system. You might have to zoom in a lot or figure out how to resize the window. Using the related function lets you focus on the x-axis to find the points.

Solving Polynomial Equations using Technology Answers

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