Questions and Answers
What are the real or imaginary solutions of the polynomial equation $x^4 - 52x^2 + 576 = 0$?
What are the real or imaginary solutions of the polynomial equation $x^3 = 216$?
Find the real solutions of the equation by graphing: $-19x^3 - 12x^2 + 16x = 0$.
0, -1.29, 0.65
Find the real solutions of the equations by graphing: $6x = 9 + x^2$.
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What are the dimensions of a shipping box at We Ship 4 You given the volume is about $7.6 ft^3$?
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Study Notes
Polynomial Equations and Solutions
- The polynomial equation (x^4 - 52x^2 + 576 = 0) has real solutions: 4, -4, 6, and -6.
- The cubic equation (x^3 = 216) yields one real solution (6) and two complex solutions: (-3 + 3i\sqrt{3}) and (-3 - 3i\sqrt{3}).
Graphical Solutions
- Graphing the equation (-19x^3 - 12x^2 + 16x = 0) reveals real solutions at 0, -1.29, and 0.65.
- The equation (6x = 9 + x^2) graphing results in a single real solution: 3.
Box Dimensions and Volume Calculation
- A shipping box's dimensions are contingent on a polynomial expression: width (x), length (x + 5), height (3x - 1).
- With a volume of approximately 7.6 cubic feet, the box's dimensions in inches are calculated as 15 inches (width), 20 inches (length), and 44 inches (height), rounding to the nearest inch.
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Test your knowledge of polynomial equations with these flashcards. Each card poses a question about finding real or imaginary solutions to different polynomial equations. Perfect for students needing to review key concepts and problem-solving techniques in algebra.
