Applying the First Theorem on Bounds for Real Zeros of Polynomials

question 23

Multiple Choice

Applying the first theorem on bounds for real zeros of polynomials, determine the smallest and largest integers that are upper and lower bounds, respectively, for the real solutions of the equation. With the aid of a graphing utility, discuss the validity of the bounds. $$3 x ^ { 4 } - 7 x ^ { 3 } - 5 x - 6 = 0$$

• A) The upper bound is \[5\] , the lower bound is \(- 3\) .
• B) The upper bound is \(3\) , the lower bound is \(- 1\) .
• C) The upper bound is \(0\) , the lower bound is \(- 2\) .
• D) The upper bound is \(1\) , the lower bound is \[- 3\] .
• E) The upper bound is \(2\) , the lower bound is \(- 4\) .

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Definitions:

Night Terror

A sleep disorder causing feelings of terror or dread, typically occurring in the first few hours of stage 3-4 non-REM sleep.

Autonomic Arousal

The automatic activation of the autonomic nervous system, influencing physiological responses such as heart rate, digestion, and respiratory rate, often in reaction to stress or excitement.

Panic

An intense, sudden onset of fear or distress, often marked by physical symptoms like rapid heartbeat and sweating.

Somnambulism

A sleep disorder characterized by walking or performing other complex behaviors while in a state of partial awakening, commonly known as sleepwalking.