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# 2.5(one) - 2.5 Zeros of Polynomial Functions Use the...

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Unformatted text preview: 2.5 Zeros of Polynomial Functions Use the Rational Zero Theorem to ﬁnd ___ossible rational zeros. The saasznataa-ra-e'rseam ' ' ' ' ' lifts} an agar" in await”- -" air-r at» nix 353w ashas:-zrrragar-ee'esfneienﬁs and it? {Whats in; manner! to toms-i: terms} ran-ratings} ram- gaff” then {I is a fact-(1s of? tha constant term, raw and gin a fawn: tiff {ha-landingenefﬁeiam, a”, 4 _ _ j: Factors-at the assistant term Pnasarbia raammal seems ”a: k . 7 ,_ _ . i ' Fastnra of the leading snails-meats List all possible rational zeros of f(X) =6X3—19X2-l—2X‘tg Starting with the integers, ﬁnd one zero of the function using synthetic division, and then factor the remaining polynomial. What are all of the zeros of the function? :t (-3 1.2.5. C» ’1'; 351. +1. +-‘—~ ‘— Q"3 ’6 + Ti ..3 2 RN m aw) Use the Rational Zero Theorem to list all of the possible zeros of f(x)=5x4 —3x3 +2x2 —x—4_ 1: 11-2-11“ M 1.15? + +§L :t :1; i2:— :3. ”}/“ ’ l+ b ‘5’ ‘5” K 1 i‘% ‘I I 5 ‘l—-—._' WW): 6X ~'1~Cix ‘P 2% "*5 H + MELLM ¥FWC _Q#H—dl+3 He) : we?» Maf—MWB :;lez E 21% 4—G'* 5 [?[’11]’:’0 E Lxrz) :3 0‘ 41““ *W' 3 6x_#qu%%ax-t3 L’X”3) 3 (a ”‘3 2 3 L +4%' “3 ’35 W e *' " [of QXQY+U~J[3X+{> CX—a) (Bx-H) (2x4): 0 %“3=D 3x+izo . lX——[:D OCH) ”51+“ ELF) 7— 9 CX‘H) U9:— Liv) : a (My) (XJraDCX 3)” >C+L2 o Solve .2. olxnomial eg nations. The Fundamum Wigwam {if Mignhm if ,1" ( 1:1 is a polynosmai {if degr’st 11, what: 11 s: ‘1 them {its squaiion f 1’ rim has at least one 1313-1119-1151: root- For 6363 —1 1x2 —x+6 = O, a) list all possible rational roots b) use synthetic division to test the possible rational roots and ﬁnd an actual root, 0) use the quotient from part b) to ﬁnd the remaining roots and solve the equation. i 1-2-3.é PaSgibLLrQi‘fU‘nai ZQ—f‘r'os :_ \$1.2,3.g_ @. 1.1. it ili3,.té,i:_;:f3 ﬁg 2,,2, 3x (21 #311291 '3) X01-” ("2x ,3) (3)91) 1’- ’ ,..- aware Find zeros of a polynomial function. ngzarﬁen of. Pnlgsun'mjagﬁ Equatimm i, Elf a polynomial equation ism? dtgme my ”than counting mniliipla- mots Sﬁgiaafﬂ'tﬁ'lﬁﬁ {333% mansion 51mm mots, _ _ . ' 2, If a + ha in a atom ‘saif at mﬁyaiomiai wanting witmwl maﬁiinitmm lib ¢ 33-. than. aha. compim imaginary ﬂﬂiﬂbﬂi‘ 9:1. -~—' it? ES 315%} a ’£‘5BGT..5 Eomgﬂw imagi~ nmy roots; if may mist, occur inmniugﬁw paim Use the Linear Factorization Theorem to ﬁnd 9 olynomials with given zeros. The Linens: Fmoﬁnaﬁunﬂwmem if ﬁx} m owx” + an?” + + ms + 11339, where a a '1 and-an as {1; than fix} m {‘99:}: " at)“: T- ﬁg)"""{£ .. {Filljé Where a; a 63‘. . , a“ are complex; wankers {msihiy mat and not necessarily aim-1m}. Ina words: its nthndegrw goiynomiai can he expressed. as the product of a nuns-em constant am} a: linear factors. Find the nth-degree polynomial function with real coefﬁcients satisfying the given conditions. ‘ 0‘ 2390 Gmci 11:4; —3,%,21jarezeros; f(2_)=_144 Remse 2L ts fa: "Hm @13an ha3 mi ’2‘: «mus-i also be a. ZPJD_ it”: (knows) (Xv-£7) (x_a:)(x+at) f ,1 on, 2: on (Ma) (Ma) (go—2f) (am) 4;.)qu 610(5) (+31) (Lia—(lit) q ...
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