Question

V I T , T.J, 4.0). This Question: 4 pts Find bounds on the real zeros of the polynomial function. f(x) = -x4 + 3x3 - 4x² - 6x + 9 The lower bound is -3,-9 and the upper bound is (Type integers or simplified fractions.) .

Answer 1

given that f1a) -+323-47°-5x-1.9 here p = t1, +3, +9 so possibilities of P .t + so possible rational roots: t1, +3, £9 fra) a f(-x) = tata a at a aant a Real zero t 3 changes & 3 or spositive l changes a negative real zeros. so by synthetic division. One will check ! -! -1 +3 - 2 -6 2 -2 -5 -2 -7 9 - upper of lower bound - 3 -4 -5 9 I -4 8 3 1 4 -8 -3 12 - -3 - 3 3 6 - 4 ass 18 66 -183 -22 61 -194 a - alternate sign so lower bound =-3 3 1 -1 3 -3 - o -4 -5 g 0 -12 ast -4 4A-42 Megative all are positive/zero so Mothing copper bound -9 -1 3 9 12 -4 -5 9 108 1008 -9027 -112 1903 -9018 + alternate sign so lower bound = -9

9 1 ~ 3 -4 -5 g I e 108 936 2379 last 5 - 12 104 931 8388 Row c'is positive & as are know if a Cast Row have all number positive or zero then c is an upper bound so 3 is upper bound, if c is negative & last now have all numbers alternately positive & negative so cis a lower bound So lower bounds are upper bounds are -3, -9 more