Question

Answer question NO.3

2) We showed a while back on a homework assignment that f(:) has a multiple root iff f(0) and f'(:1) have a common factor. That means that Res( f(:1), f'(:)) = 0. Verify this with f(x) = 1 – 3.1 +2. 3) It can be shown that in general the discriminant of a polynomial f (:) is (up to a sign) Res(2), f'.)). Use the resultant to verify the formula we gave for f(1) = r +pr+q on homework 7.2. (note that with this and problem 2, we see that the discriminant tells us when a polynomial has a multiple root).

Answer 1

f(x) = x²-3x+2 let #Given that Now ful= won²+x²-n-2n+2 = 0 n?-) ) + n(n-1) -2 (1-1) = 0 - (2-1) in ²+u-2) = 0 = (x-7) (n² + 2M-n-2)=0 =) (-1)} Uni2) 1 (1+2)} =0 -) (-04-1)(+2) = 0. f'no = 3² - 3 Let el'in =0 = 30²-3=0 - 3 (221)=0 =) 3 (utll (27) 20. Here fm) has a two times root at n=1 but flow has a root at =) once. so Res (fin), f(n)) = 0.