Question

Use the rational zeros theorem to list all possible rational zeros of the following.

g(x) = 2x4 – 7x + 4x2 + 3x - 5
Be sure that no value in your list appears more than once.

Answer 1

To find the potential rational zeros for the polynomial g(x) = 2x^4 – 7x^3 + 4x^2 + 3x - 5, list the factors of the constant term divided by the factors of the leading coefficient, and make sure to list each zero only once.

Step-by-step explanation:

The Rational Zeros Theorem helps you list all potential rational zeros of a polynomial. For the polynomial g(x) = 2x4 – 7x3 + 4x2 + 3x - 5, list the possible rational zeros by taking all the factors of the constant term (5) and dividing them by the factors of the leading coefficient (2). To simplify the algebra, eliminate any duplicates in your list of possible zeros. Finally, check that the list is reasonable and includes all the possibilities based on the theorem.Factors of the constant term 5 are ±5 and ±1. Factors of the leading coefficient 2 are ±2 and ±1. The possible rational zeros are ±5/2, ±5, ±1/2, and ±1. Make sure that each zero is listed only once.