No. Your work shows there are no rational roots, but there could be real or complex roots.Firepanda said:f(t) = t4 - 23 + 3t2 - 2t + 1 in Q[t]
Am i right in thinking I just show by the rational root theorem that the only possible roots are +-1
Firepanda said:f(+-1) =/= 0 so there are no repeated factors?
Seems too easy..
A repeated factor in a polynomial is a factor that appears more than once in the polynomial. For example, in the polynomial 2x^2 + 4x + 2, the factor (x+1) appears twice, making it a repeated factor.
To determine if a polynomial has a repeated factor, you can factor the polynomial and look for factors that appear more than once. Another way is to check the degree of each factor - if it is greater than 1, it is a repeated factor.
Knowing if a polynomial has a repeated factor can help in simplifying the polynomial and finding its roots. Repeated factors can also provide information about the behavior of the polynomial and can help in graphing it.
Yes, a polynomial can have more than one repeated factor. For example, the polynomial (x+1)^3 would have the repeated factor (x+1) three times.
If you find a repeated factor in a polynomial, you can use the repeated factor theorem to simplify the polynomial and find its roots. This theorem states that if a polynomial has a repeated factor, the root associated with that factor will have a multiplicity greater than 1.