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
64
1
avatar

Let f(x) be a quartic polynomial with integer coefficients and four integer roots. Suppose the constant term of f(x) is 6.

(a) Is it possible for x=3 to be a root of f(x)?

(b) Is it possible for x=3 to be a double root of f(x)?

 

Prove the answer. 

 

I really help and ASAP, please answer this for me. I do not understand this problem at all.

 Aug 11, 2019
 #1
avatar+28134 
+1

"Let f(x) be a quartic polynomial with integer coefficients and four integer roots. Suppose the constant term of f(x) is 6.

(a) Is it possible for x=3 to be a root of f(x)?"

 

(a)   (x+1)2(x-2)(x-3)   constant term is 6

 

"(b) Is it possible for x=3 to be a double root of f(x)?"

(x-3)2(x-a)(x-b)   constant term is 9ab   Therefore not possible for this to be 6 if a and b are integers.

 Aug 11, 2019

34 Online Users

avatar
avatar
avatar
avatar
avatar