The roots of f(x) are 3, 4, and 2. What are the roots of f(x^2+1)

Question

please show work

Answer 1

If the roots of f(x) are 3, 4, and 2, then:

 

       f(x) = a(x-4)(x-3)(x-2) 

 

where a is a non-zero constant.  So:

 

     f(x²+1) = a(x²+1-4)(x²+1-3)(x²+1-2)

     f(x²+1) = a(x²-3)(x²-2)(x²-1)

 

The roots occur when f(x²+1) = 0:

 

     0 = a(x²-3)(x²-2)(x²-1)

     x = ±√3, ±√2, ±1