+0  
 
0
430
3
avatar

idk if the upload of the picture worked (if it didnt someone help me understand how to use it)

Find k if the remainder is 3 when 5x^2-10x+k is divided by x-1

I have several questions like this one so im more looking for an explanation than a solution :) thank you!

Guest Jun 1, 2015

Best Answer 

 #2
avatar+26750 
+10

If 5x2 - 10x + k has remainder 3 when divided by x - 1 then we must have:

 

5x2 - 10x + k = (x - 1)*m + 3  where m is an integer.

 

When x = 1 the right-hand side is just 3 and m disappears so put x = 1 in the left-hand side as well to get

 

5 - 10 + k = 3

 

or k = 8

 

(Chris beat me to it!)

 

Incidentally, you can't upload images as long as you stay Anonymous.  Why not register, then you will have access to the upload images function.

 

.

Alan  Jun 1, 2015
 #1
avatar+87301 
+10

 

 

Notice that if we substituted 1 into the polynomial, we could find the value of k that would make 1 a root....in other words, we could find the k value such that, P(1) = 0....... (or, put another way, would make (x-1) a divisor of the polynomial with no remainder).......

 

So.....using the same idea.......we want to find the value of k that makes P(1)  = 3

 

So P(1)  =  5(1)^2 - 10(1) + k = 3   →  5 - 10 + k = 3  →  -5 + k = 3 →  k = 8

 

Test this for yourself using synthetic division.......you will find that you get a remainder of 3 when k = 8 and you divide by 1.....

 

CPhill  Jun 1, 2015
 #2
avatar+26750 
+10
Best Answer

If 5x2 - 10x + k has remainder 3 when divided by x - 1 then we must have:

 

5x2 - 10x + k = (x - 1)*m + 3  where m is an integer.

 

When x = 1 the right-hand side is just 3 and m disappears so put x = 1 in the left-hand side as well to get

 

5 - 10 + k = 3

 

or k = 8

 

(Chris beat me to it!)

 

Incidentally, you can't upload images as long as you stay Anonymous.  Why not register, then you will have access to the upload images function.

 

.

Alan  Jun 1, 2015
 #3
avatar+87301 
0

That's OK, Alan.....you gave me 3 points....I'll give you 3......!!!

 

CPhill  Jun 1, 2015

8 Online Users

avatar

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.