ROOTS of Polynomials

Front

What is a root of a polynomial?

Back

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

Front

How many roots can a polynomial of degree n have?

Back

A polynomial of degree n can have up to n roots.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial has at least one complex root.

Front

What are real roots?

Back

Real roots are the values of x where the polynomial intersects the x-axis.

Front

What are imaginary roots?

Back

Imaginary roots are roots that cannot be expressed as real numbers and occur in complex conjugate pairs.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c.

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree 3, typically in the form ax^3 + bx^2 + cx + d.

Front

How can you determine the number of real roots of a quadratic polynomial?

Back

You can determine the number of real roots using the discriminant (b^2 - 4ac). If it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the relationship between the roots and the coefficients of a polynomial?

Back

The roots of a polynomial are related to its coefficients through Vieta's formulas, which relate the sums and products of the roots to the coefficients.

Front

What does it mean for a polynomial to have multiple roots?

Back

A polynomial has multiple roots when a root occurs more than once, indicating that the graph touches the x-axis at that point.