Solving Polynomial Equations using Technology

Question 1

The following system of equations can be used to find the roots of the equation x3 + 72 = 5x2 + 18x.y = x3 + 72y = 5x2 + 18xGraph this system of equations on the graphing calculator.How many intersection points can you see in the default viewing window? ✔ 123

Revolt · Accepted Answer

✔ 1

Question 2

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.

Question 3

Adjust the window so you can find all of the points of intersection for the system of equations.What are the roots of the original polynomial equation? Check all that apply.

Revolt · Accepted Answer

–6; 0; 6; –4; 3; 8

Question 4

From least to greatest, what are the roots of the polynomial equation?

Revolt · Accepted Answer

-3, -2, 4; -2, 3, 4; 2, 3, 5

Question 5

Which system of equations can you use to find the roots of the equation 2x3 + 4x2 – x + 5 = –3x2 + 4x + 9?

Revolt · Accepted Answer

y = 2x3 + 4x2 – x + 5 y = –3x2 + 4x + 9

Question 6

Use a graphing calculator and a system of equations to find the roots of the equation. x4 − 4x3 = 6x2 − 12x From least to greatest, what are the integral roots of the equation? and

Revolt · Accepted Answer

"-2"; A

Question 7

What are the approximate values of the non-integral roots of the polynomial equation?

Revolt · Accepted Answer

–1.95

Question 8

A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form an open box. The volume of the box is 420 in.3.The equation 4x3 – 72x2 + 320x = 420 can be used to find x, the side length of the square cut from each corner.What is the side length of the square that is cut from each corner, to the nearest inch? ⇒ 3 in.

Revolt · Accepted Answer

PENDING

Question 9

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.

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