Sect. 5.1 Finding Zeros using Rational Root Theorem

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that if a polynomial has a rational root (p/q), then p is a factor of the constant term and q is a factor of the leading coefficient.

Front

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

Back

List all factors of the constant term and the leading coefficient, then form all possible fractions p/q.

Front

What are the possible rational roots for the polynomial 2x^3 - 11x^2 + 12x + 9 = 0?

Back

±1, ±3, ±9, ±1/2, ±3/2, ±9/2.

Front

Solve for x using the Rational Root Theorem: x^3 + 3x^2 - 6x - 8 = 0.

Back

x = -4, -1, 2.

Front

Identify a rational root for the polynomial f(x) = x^3 + 2x^2 - 11x - 12.

Back

x = -4.

Front

What is a polynomial equation?

Back

A polynomial equation is an equation that equates a polynomial expression to zero.

Front

What is a zero of a polynomial?

Back

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

Front

Find all real solutions of the polynomial equation x^3 - 3x^2 - 2x + 4 = 0.

Back

x = 1, 1 ± √5.

Front

Find all real solutions of the polynomial equation x^3 - 3x^2 + 2 = 0.

Back

x = 1, 1 ± √3.

Front

What is the significance of finding zeros in polynomial functions?

Back

Finding zeros helps in understanding the behavior of the polynomial graph and solving equations.