Fundamental Theorem of Algebra (Edited)

Front

What does the Fundamental Theorem of Algebra state?

Back

Every non-constant polynomial equation has at least one complex root.

Front

How do you find the zeros of a quadratic function?

Back

You can find the zeros by factoring, using the quadratic formula, or completing the square.

Front

What are the zeros of the polynomial f(x) = x^2 + 9x + 14?

Back

The zeros are -2 and -7.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.

Front

What is the result of (4x^2 - 24x + 35) ÷ (2x - 5)?

Back

The result is 2x - 7.

Front

What is the significance of imaginary roots in polynomials?

Back

Imaginary roots always come in conjugate pairs.

Front

How do you determine the zeros of a polynomial given one factor?

Back

You can use synthetic division to divide the polynomial by the given factor and then find the zeros of the resulting polynomial.

Front

If (x - 5) is a factor of f(x) = x^3 - 2x^2 - 13x - 10, what are the other factors?

Back

The other factors are (x + 2) and (x + 1), so f(x) = (x - 5)(x + 2)(x + 1).

Front

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

Back

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

Front

What is the quadratic formula?

Back

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