
Concept explainers
a.
To find: the value of the time for which the polynomial equation f(t)=0 .
a.

Answer to Problem 74PPS
x3−12x2+4x−48=0 .
Explanation of Solution
Given:
A population of parasites in an experiment can be molded by f(t)=t3+5t2−4t−20 .
Calculation:
As the polynomial equation is f(t)=t3+5t2−4t−20 .
Now, to find the factor of the equation where f(t)=0 . Therefore,
f(t)=t3+5t2−4t−20 {given polynomial}t3+5t2−4t−20=0 {given f(t)=0}t2(t+5)−4(t+5)=0 {taking (t+5)as common}(t+5)(t2−4)=0 {use distributive property of product}
Either (t+5)=0 or (t2−4)=0
When (t+5)=0 , then t=−5
When (t2−4)=0 , then t2=4 ⇒t=±√4=±2
Hence, the value of time is t=−5,−2,2 .
b.
To find: the value of x by using the polynomial factor.
b.

Answer to Problem 74PPS
2 days.
Explanation of Solution
Given:
A population of parasites in an experiment can be molded by f(t)=t3+5t2−4t−20 .
Calculation:
From part (a), the time is t=−5,−2,2 .
This means there are 3 results which are t=−5,−2,2 .
Since the days is not negative, so the time when population reach zero, is 2 days
Since, (x2+4) cannot be zero, therefore, (x−12)=0 is zero.
⇒x=12
Hence, the value of x=12 .
c.
To check: that for any value of t is unreasonable.
c.

Answer to Problem 74PPS
t=−5,−2 .
Explanation of Solution
Given:
A population of parasites in an experiment can be molded by f(t)=t3+5t2−4t−20 .
Calculation:
From part (a), the time is t=−5,−2,2 .
This means there are 3 results which are t=−5,−2,2 .
Since the days is not negative, Hence, the value of t=−5,−2 is unreasonable.
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