Rational Zero Theorem

Front

What is the Rational Zero Theorem?

Back

The Rational Zero Theorem states that if a polynomial has rational roots, they can be expressed as the ratio of the factors of the constant term to the factors of the leading coefficient.

Front

List the possible rational roots of the polynomial: 2x^3 - 11x^2 + 12x + 9 = 0.

Back

±1, ±3, ±9, ±1/2, ±3/2, ±9/2.

Front

True or False: All imaginary roots come in pairs.

Back

True.

Front

What should you do if you are missing an exponent in your polynomial?

Back

You must put a zero as a coefficient placeholder for that exponent.

Front

Identify a possible root of the polynomial: x^3 - 6x^2 - x + 30.

Back

-15.

Front

What are the factors of the constant term in the polynomial 3x^2 + x + 7?

Back

The factors are ±1, ±7.

Front

What are the factors of the leading coefficient in the polynomial 3x^2 + x + 7?

Back

The factors are ±1, ±3.

Front

If a polynomial has a degree of 3, what is the maximum number of real roots it can have?

Back

It can have a maximum of 3 real roots.

Front

What is the significance of the Rational Root Theorem in polynomial equations?

Back

It helps in identifying possible rational roots, which can simplify the process of finding actual roots.

Front

True or False: The Rational Root Theorem can only be applied to polynomials with integer coefficients.

Back

True.