27
practice examMultiple Choice

Practice Exam

Question 27 • Algebra II

You can use a system of equations to graph and solve the polynomial equation 3 x cubed plus x is equal to 2 x squared plus 1 Which statement is true?

Answer
A
The y -coordinates of the solutions to the system and the zeroes of the equation are not equal.
B
The equation has one zero, and the system has three solutions.
C
The system has one solution, and the equation has three zeroes.
D
The x -coordinates of the solutions to the system and the zeroes of the equation are not equal.

Explanation

Graph the two sides as y = 3x³ + x and y = 2x² + 1. Their intersections have x-coordinates that solve 3x³ + x = 2x² + 1, so those x-coordinates are the equation’s zeroes when the equation is written as 3x³ − 2x² + x − 1 = 0. The intersection’s y-coordinate is not that zero: for example, the equation’s real zero is about 0.78, while the corresponding y-coordinate is about 2.22. Thus the true statement is that the y-coordinates and zeroes are not equal.

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