Find All Rational Zeroes of the Function Given and Use

question 112

Multiple Choice

Find all rational zeroes of the function given and use them to write the function in factored form. Use the factored form to state all zeroes of the function. Begin by applying the tests for 1 and -1. p(x) = 4x⁴ + x³ + 33x² +9x - 27

• A) p(x) = (x - 1)(4x - 3)(x - 3i)(x + 3i); zeroes: 1, , 3i, -3i
• B) p(x) = (x - 1)(4x + 3)(x - 3i)(x + 3i); zeroes: 1, - , 3i, -3i
• C) p(x) = (x + 1)(4x - 3)(x - 3i)(x + 3i); zeroes: -1, , 3i, -3i
• D) p(x) = (x + 1)(4x + 3)(x - 3i)(x + 3i); zeroes: -1, - , 3i, -3i

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Definitions:

Exponents

mathematical operations denoting how many times a number, the base, is multiplied by itself.

Marginal Products

The increase in output resulting from a one-unit increase in the quantity of a single input, keeping others constant.

Exponents

Mathematical notation indicating the number of times a number (the base) is multiplied by itself.

Production Function

A model in economics that links physical output of a production process to physical inputs or factors of production.