### All SAT II Math II Resources

## Example Questions

### Example Question #541 : Sat Subject Test In Math Ii

A polynomial of degree 4 has as its lead term and has rational coefficients. One of its zeroes is ; this zero has multiplicity two.

Which of the following is this polynomial?

**Possible Answers:**

Cannot be determined

**Correct answer:**

A fourth-degree, or *quartic*, polynomial has four zeroes, if a zero of multiplicity is counted times. Since its lead term is , we know by the Factor Theorem that

where the terms are the four zeroes.

A polynomial with rational coefficients has its imaginary zeroes in conjugate pairs. Since is such a polynomial, then, since is a zero of multiplicity 2, so is its complex conjugate . We can set and , and

We can rewrite this as

or

Multiply these factors using the difference of squares pattern, then the square of a binomial pattern:

Therefore,

Multiplying:

### Example Question #542 : Sat Subject Test In Math Ii

Find the roots to:

**Possible Answers:**

**Correct answer:**

This equation cannot be factored. Since this is a parabola, we can use the quadratic equation to find the roots.

Substitute the coefficients of .

The answers are: