Descartes' Rule of Rational Root Theorem and Finding All Zeros

A Polynomial of Degree 6 CAN have the following number of imaginary roots:

• 1
• 4
• 3
• 8

How many roots does the following function have?

f(x)= x⁵ - 3x³ + x

• 8

• 9

• 5

• 3

What is the name of the polynomial that has 4 roots?

• Quadratic

• Quartic

• Cubic

• Quintic

How many possible negative real solutions does the following polynomial have?

f(x) = x⁴ - 3x³ - 17x² + 39x -20

• 3 or 1

• 3

• 1

• 2 or 0

How many possible positive real solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

• 4, 2, or 0

• 4

• 3 or 1

• 3

• 3 real positive, 2 real negative, 0 imaginary

• 0 real positive, 1 real negative, 4 imaginary

• 1 real positive, 2 real negative, 2 imaginary

• 1 real positive, 0 real negative, 4 imaginary

Descartes was from _______.

• Sweden

• Germany

• England

• France

Despite all of his contributions to math, Descartes is ofter referred to as "The Father of Modern _____________.

• Science

• Philosophy

• Education

• Mathematics

Descartes biggest contribution to math was the development of __________________.

• rules of exponents

• the use of variables

• the Cartesian coordinate system

• the Polar coordinate system

Descartes' Rule of Signs is helpful is solving what kind of equation?

• rational

• exponential

• logarithmic

• polynomial