+0  
 
+1
309
2
avatar

Write a Polynomial f(x) in complete factored form that satisfies the conditions: The leading coefficient is 10. The degree is 6. there is a zero at 2 with multiplicity 3, a zero at 6 with multiplicity 1 and a zero of 5i.

Guest May 1, 2017
 #1
avatar+249 
+2

\(f(x)= ?\)

 

There is a zero at 2 with multiplicity 3

\(f(x) = (x-2)^3 (?)\)

 

 A zero at 6 with multiplicity 1

\(f(x)= (x-2)^3(x-6)(?)\)

 

A zero of 5i

\(f(x)=(x-2)^3(x-6)(x^2+25)\)

 

It is good to note that complex factors come in pairs so by adding a complex factor you essentially solve for two complex zeroes                                                                         

 

Now we have a polynomial with a degree of 6. However, we need the leading coefficient to be 10. To do this we just include a ten as a subset of the function like this. \(f(x)=10(x-2)^3(x-6)(x^2+25)\)  Now you have a polynomial f(x) that satisfies all the given conditions. smiley

JonathanB  May 1, 2017
 #2
avatar+26750 
+1

Good answer! Though since the question asks for the complete factored form you might replace the \((x^2+25)\)  term by  \((x-5i)(x+5i)\)

Alan  May 1, 2017

15 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.