We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
141
7
avatar

A polynomial with integer coefficients is of the form \(7x^4 + a_3 x^3 + a_2 x^2 + a_1 x - 14 = 0\). Find the number of different possible rational roots of this polynomial.

 May 21, 2019
 #1
avatar+105704 
0

 

I might be simplifying this too much but there can only be a maximum of 4 becasue 4 is the degree.

Maybe there is less than 4

 May 21, 2019
edited by Melody  May 21, 2019
 #2
avatar
+1

I don't think you umderstood the question. The guest is not asking for the maximal amount of rational roots the polynomial can have.

Guest May 21, 2019
 #3
avatar+105704 
0

Yes ok   laugh

Melody  May 21, 2019
 #4
avatar+6045 
+2

any rational roots are a factor of the constant term divided by a factor of the coefficient of the highest degree term.

 

here the constant term is -14 with factors +/- 1, +/- 2, +/- 7 +/- 14

and the leading coefficient is 7 with factors +/- 1, +/- 7

 

thus we have possible rational roots

 

+/- 1/7

+/- 2/7

+/- 1

+/- 2

+/- 7

+/- 14

 

a total of 12 possible rational roots

Rom  May 21, 2019
edited by Rom  May 21, 2019
edited by Rom  May 21, 2019
 #5
avatar
+2

Isn't 14 a factor of 14 too?

Guest May 21, 2019
 #6
avatar+6045 
+2

sigh, it sure is.  Add 14 and -14 to the list bringing it to 12 possible rational roots.

Rom  May 21, 2019
 #7
avatar+105704 
0

Thanks Rom,

I didn't know that, I shall try and remember.   laugh

 

 

I mean I did not know this...

Any rational roots are a factor of the constant term divided by a factor of the coefficient of the highest degree term.

Melody  May 23, 2019
edited by Melody  May 23, 2019

8 Online Users

avatar