Fundamental Theorem of Algebra

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What is the Fundamental Theorem of Algebra?

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The Fundamental Theorem of Algebra states that every non-constant polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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What is a polynomial?

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A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero.

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If 2i is a zero of a polynomial, what can be inferred about its roots?

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If 2i is a zero, then -2i must also be a zero due to the complex conjugate root theorem.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

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How do you find the remainder in synthetic division?

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The remainder is found by evaluating the polynomial at the root of the divisor.

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What is the quadratic formula?

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The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

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What does it mean for a polynomial to have a degree of n?

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The degree of a polynomial is the highest power of the variable in the polynomial.

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient determines the end behavior of the polynomial function as x approaches ±∞.

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What is the relationship between the degree of a polynomial and the number of roots?

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A polynomial of degree n will have exactly n roots in the complex number system, counting multiplicities.