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# Quiz_sol - Student’s Namezl Signature Quiz 4 Section 3.4...

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Unformatted text preview: Student’s Namezl Signature: Quiz 4: Section 3.4 7 5 ” 1 Reminder of the Factor Theorem 7‘ is a zero of the polynomial f (m) <=> f (r) = O ¢=> the term (m -— r) is a. LINEAR factor of f. 2 Question 1 (5 points) This is the Example 6 in the lecture notes of Section 3.4. [3.4.1cPT]Fin}i the leading coefﬁcient, A, of the polynomial f(1‘) = Ah: — r1)(:c — r2)(a: — T3) with zeros -3, -2, l. and f(—4).= 15. _ J: i ﬁx) = A(X+5\(Mz\(,,‘\ g mu 10+): lg I: ;5 % A ('“t33C-H 1-7.\(~q-h % A(—\o\ : L5 :3 2.; : A (~l)(~z¥—s\ is) A : |S/_‘o 42 : A (do) A : -3 Hints: x:—L\ irﬁo ~‘-> /’2. o What are the given zeros? Then, what are the factors (a; — r1), (1‘ — r2), (1: — 73)? Or in other words, according to the Factor Theorem, what are r1, 7-2, 1-3? 0 Rewrite f (x) with the known 7‘1, r2, r3. 0 What is the extra information in the question that you have not used? 0 Then, what does it mean by f(—4) = 15? It means f(—4) = A(a:—r1)(z—r2)(a:—r3) =’ 15 with x = —4. Can you ﬁnd the leading coeﬁicient A frozn here? 3 Question 2 (5 points) This is the Example 7 in the lecture notes of Section 3.4. [3.4.1dPT]Find k such that ﬁx) = 2 — 2kg: — 212 km“ h factor of (at—2). _ (If!) av . > ' C => v.1 is Hm Zero dr g; Manama -ZC7.)7’— i413) => -FL?—):Z‘qk ‘3—3‘( 1% 0 "’ "'"u .=-:> G='\ZK%K: :—)é/ 4 n I n i mu can» me: "In Hints: o What can you tell about the number 2 if (x — 2) is a. factor of f? 0 According to the Pastor Theorem, f (2) = 0. Can you ﬁnd I: from here? ...
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