Use the Intermediate Value Theorem to Determine Whether the Polynomial

question 82

Multiple Choice

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-f(x) = x⁵ - 10x⁴ + 42x³ -124 x² + 297x - 306 ; zero: 3i

• A) 2, -3i, 4 - i, 4 + i
• B) -2, -3i, -4 - i, -4 + i
• C) 2, -3i, -4 - i, -4 + i
• D) -2, -3i, 4 - i, 4 + i

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Definitions:

Crossed Claisen Condensation

A reaction between different esters or an ester and a carbonyl compound under basic conditions to form a β-keto ester or a β-diketone.

Methyl Benzoate

A compound consisting of a methoxy group (-OCH3) attached to a benzene ring substituting a hydrogen atom.

Cyclohexanone

A ketone with a six-membered ring structure, used as an important solvent and in the synthesis of nylon and other polymers.

Sodium Ethoxide

An organic compound and strong base, formulated as C2H5ONa, used in organic synthesis, particularly for the deprotonation of weaker acids.