Fundamental Theorem of Algebra

The number of COMPLEX ROOTS is the same as the degree of the function

• TRUE

• FALSE

Answer explanation

Remember that the degree is the highest exponent in standard form. The degree tells you how many complex roots (zeros) the function will have. Complex roots can be real and/or imaginary. REAL roots you can see on a graph.

The number of TURNS in a graph is the same as the DEGREE of the function

• TRUE

• FALSE

Answer explanation

The number of turns is always 1 less than the degree. If a graph has 2 turns, then it is a degree 3 function.

Determine the degree according the given a graph and a function.

f(x) = 3x - 4x³ + 2

• 3

• 4

• 5

• 6

IMAGINARY ROOTS and IRRATIONAL ROOTS come in conjugate pairs

• TRUE

• FALSE

Answer explanation

You will never have an ODD NUMBER of imaginary or irrational roots. You can have none, 2, 4, 6, ... but never 1, 3, 5, ....

Determine the number of COMPLEX ROOTS according to the given graph and function.

f(x) = 3x - 4x³ + 2

• 3

• 4

• 5

• 6

Determine the number of REAL solutions according the graph and function.

f(x) = 3x - 4x³ + 2

• 0

• 1

• 2

• 3

Determine the number of IMAGINARY solutions according the graph and function.

f(x) = 3x - 4x³ + 2

• 1

• 2

• 3

• 4

Determine the degree according to the graph

• 3

• 4

• 5

• 6

Mathematical Equivalence

ON

Determine the number of REAL ROOTS factors from the given graph and function.

f(x) = 3x - 4x³ + 1

• 1

• 2

• 3

• 4

Answer explanation

Remember that a bounce on the x axis means multiplicity of 2 - that root is a double root and counts twice.