Algebra 2 Polynomial Roots Quiz and Flashcards

Questions and Answers

What is the root of a polynomial?

A value for the variable of a polynomial that makes the polynomial equal to zero.

To find the roots of a polynomial, it is often useful to find the ____ of the polynomial.

factors

What is the result of multiplying the matrices |1,2,3| and |3,1,-1|?

Roots of a polynomial are the values that make the polynomial equal to ___.

zero Signup and view all the answers

_____ number roots of a polynomial are the points where the graph of the related polynomial function crosses the x-axis.

Real Signup and view all the answers

What is f(g(x)) if f(x)=3x+5 and g(x)=5x-1?

15x + 2 Signup and view all the answers

What is the nature of the roots of the equation y=x²+4?

No real roots Signup and view all the answers

If abc=0, then ___.

a=0 or b=0 or c=0 Signup and view all the answers

How many real roots are there in y=x³-3x²+x-3 based on the graph description (left down right side up)?

3 Signup and view all the answers

What are the correct roots of the polynomial equation x³+4x²-11x-30=(x+2)(x-3)(x+5)=0?

x=-2, 3, -5 Signup and view all the answers

What are the roots of the polynomial equation (2x+3)(3x-5)=0?

-5/3 and -3/2 Signup and view all the answers

Where does the graph of the polynomial function f(x)=x²+5x+6 cross the x-axis?

x=-2, -3 Signup and view all the answers

Use the quadratic formula to find the roots of the quadratic equation y=x²+x+1.

x=-1/2±i√3/2 Signup and view all the answers

Study Notes

Polynomial Roots

Roots of a polynomial are the values that make the polynomial equal to zero.
Real number roots represent points where the polynomial's graph intersects the x-axis.

Finding Roots

To find polynomial roots, identifying factors of the polynomial proves useful.
If the product of factors equals zero (abc=0), then at least one factor must be zero (a=0, b=0, or c=0).

Graph Analysis

The function y=x²+4 has a minimum value of 4, indicating it has no real roots since it doesn't intersect the x-axis.
The graph of the polynomial function f(x) = x² + 5x + 6 crosses the x-axis at x = -2 and x = -3.

Matrix Multiplication

Matrix multiplication for |1,2,3| and |3| results in |2|.

Function Composition

For functions f(x) = 3x + 5 and g(x) = 5x - 1, the composition f(g(x)) equals 15x + 2.

Root Calculation Examples

The real roots for y=x³-3x²+x-3 can be obtained by graph inspection, yielding three roots.
The polynomial equation x³+4x²-11x-30 can be factored into (x+2)(x-3)(x+5), with roots x = -2, 3, and -5.
The roots of the equation (2x+3)(3x-5)=0 are found to be x = -3/2 and x = 5/3.

Quadratic Formula

Using the quadratic formula, roots for the equation y=x²+x+1 are x = -½ ± i√3/₂, indicating complex roots.

Description

Test your understanding of polynomial roots and matrices with these flashcards from Algebra 2 Unit 6 Lesson 5. Each card presents key definitions and concepts that are essential for mastering algebraic principles. Perfect for quick revision and retention of important terms!