+0  
 
+1
169
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
Sort: 

2+0 Answers

 #1
avatar+245 
+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+26366 
+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

4 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details