Questions and Answers
Find all the roots of the equation $X^3 + x^2 + 4x + 4 = 0$.
-1, +2i
Find all the roots of the equation $X^3 + 4x^2 + x - 6 = 0$.
-3, -2, 1
What are the roots of the function?
2, +√3
What are the roots of the function?
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What are the roots of the function?
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What are the roots of the function?
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What are the roots of the function?
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Find all the roots of the equation $X^3+x^2+4x+4=0$.
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Find the roots of the equation $X^3+4x^2+x-6=0$.
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Find the roots of a polynomial that satisfies the conditions provided in the definition.
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Find the roots of a polynomial that satisfies the conditions provided in the definition.
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Find the roots of a polynomial that satisfies the conditions provided in the definition.
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Find the roots of a polynomial that satisfies the conditions provided in the definition.
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Find the roots of a polynomial that satisfies the conditions provided in the definition.
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Determine whether the following statement is always, sometimes, or never true: A polynomial function with real coefficients has real zeros.
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Determine whether the following statement is always, sometimes, or never true: A polynomial function that does not intercept the X-axis has complex roots only.
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Determine whether the following statement is always, sometimes, or never true: An odd degree polynomial function with real coefficients has at least one real root.
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Study Notes
Roots of Polynomial Equations
- The equation ( X^3 + X^2 + 4X + 4 = 0 ) has roots at -1 and ( +2i ).
- The equation ( X^3 + 4X^2 + X - 6 = 0 ) has roots at -3, -2, and 1.
- A third example yields roots at 2 and ( +\sqrt{3} ).
- An additional equation has roots at ( +2 ) and ( +\sqrt{2} ).
- The equation with roots at -6 and ( +i ).
- Another polynomial has roots at -2 and ( 3 + i\sqrt{2} ).
- Another polynomial found roots at -2, 3, and ( +i ).
Statements About Polynomial Functions
- A polynomial function with real coefficients has real zeros sometimes.
- A polynomial function that does not intercept the x-axis always has complex roots only.
- All polynomial functions of degree greater than zero with real coefficients always have at least one real root.
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Description
Test your understanding of the Fundamental Theorem of Algebra with these practice flashcards. Solve various polynomial equations and find their roots without using a calculator. This quiz will help reinforce your skills in identifying complex and real roots.
