Overview of zeros of a polynomial - Online Tutor - Free Math Videos

The video tutorial covers the concept of zeros in polynomials, explaining their significance and how to find them using various mathematical theorems and rules. It discusses the fundamental theorem of algebra, the rational root theorem, Descartes' rule of signs, and the role of complex conjugates in identifying polynomial roots. The use of graphing calculators and synthetic division is also highlighted as essential tools in solving polynomial equations.

What is another term used for the zeros of a polynomial?

• Coefficients

• Roots

• Intercepts

• Vertices

According to the Fundamental Theorem of Algebra, how many factors does a polynomial of degree greater than one have?

• None

• Exactly two

• Infinite

• At least one

What does the Linear Factorization Theorem state about the number of factors a polynomial can have?

• Equal to the degree

• Less than the degree

• More than the degree

• Unrelated to the degree

What does the Rational Root Theorem help determine?

• Possible rational roots

• Complex roots

• Imaginary roots

• Real roots

How do you find possible rational roots using the Rational Root Theorem?

• Divide factors of the leading coefficient by the constant

• Subtract factors of the constant from the leading coefficient

• Divide factors of the constant by the leading coefficient

• Multiply factors of the constant and leading coefficient

What does Descartes' Rule of Signs help determine?

• Number of imaginary roots

• Number of rational roots

• Number of positive and negative real roots

• Number of complex roots

How do you determine the number of possible positive real roots using Descartes' Rule of Signs?

• Count the coefficients

• Count sign changes in the polynomial

• Count the degree of the polynomial

• Count the number of terms

What is true about complex conjugates in relation to polynomial roots?

• Both are roots if one is a root

• They cancel each other out

• Only one can be a root

• They are not related

If a polynomial has a root of 3 + 2i, what is another root?

• 3 + 2i

• 3 - 2i

• -3 - 2i

• -3 + 2i

Why is it important to consider both a complex number and its conjugate when identifying zeros?

• They are both zeros

• They are always equal

• They are imaginary

• They are not zeros