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
79
2
avatar+84 

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 your answers.

 Apr 30, 2019
 #1
avatar+5232 
+2

\(\text{all the roots are integers so we have}\\ f(x) = (x-i_1)(x-i_2)(x-i_3)(x-i_4)\\ \text{The constant term is }c_0 = i_1 i_2 i_3 i_4 = 6\\ \text{3 can be a root as }3\cdot 2 = 6\\ \text{On the other hand 3 cannot be a double root as }3\cdot 3 = 9\\ \text{and there is no combination of integer factors that will multiply 9 to obtain 6}\)

.
 May 1, 2019
 #2
avatar+84 
+2

Thank you this response is short and to the point while still helping me understand the problem

 May 2, 2019

13 Online Users

avatar