Question about theorems and roots of polynomial equations?? :(
1. use the rational root theorem to list all possible rational roots of the polynomial equation x^3-x^2-x-3=0 do not find the actual roots (1 point)
-3,-1,1,3
1,3
-33
no roots

Question

Question about theorems and roots of polynomial equations?? :(
1. use the rational root theorem to list all possible rational roots of the polynomial equation x^3-x^2-x-3=0 do not find the actual roots (1 point)
-3,-1,1,3
1,3
-33
no roots

anonymous · Answer

http://www.purplemath.com/modules/rtnlroot.htm Try looking at this if my explanation does not help. So the theorem basically states that for a polynomial, look at its constant term, in this case -3, and find all its factors and also find all the factors of the coefficient of the term with greatest power which is 1 because coefficient of x^3 is 1. So factors of -3 are +/- 1, +/-3 and factors of 1 is well 1. Since our leading coefficient is 1, there is no point of including values such as (+/-1 ) / 1 as part of our potential roots because it is already considered. In this case, answer is A, but if the coefficient of highest power was 2, then potential roots would also be +/- (1/2) and +/- (3/2) along with +/-1 and +/-3.