Unknown
Answers to Exercises; Chapter (^6 343) = t6 - (Cmn)t5 + (Cm2np + 3mnpq)t4 (Cm3npq + 2Cm2n2pq + Cm2n2p2)t3 (Cm3n2p2q + 3m2n2p2 ...
344 Answers to Exercises and Solutions to Problems a0 # 0, the sum of the reciprocals of the squares of the zeros is (a1/ao)2 - ...
Answers to Exercises; Chapter 6 345 Substituting for u and v yields (2a3 - gab) - (2a2 - 6b)dG 5 -27~ 5 (2a3 - gab) -I- (2a2 - 6 ...
346 Answers to Exercises and Solutions to Problems (b) First solution. Suppose the zeros are a, 6, c, d with a + b = c+ d = -p/2 ...
Answers to Exercises; Chapter 6 347 2.5. Let the zeros of t3 + at2 + bt + c be 2, y, z. Then D = (r - Y)~(z - z)~(Y - z)~ = Cx4y ...
348 Answers to Exercises and Solutions to Problems Solutions to Problems Chapter 6 4.1. (a) If the roots are r - s, r, T + s, th ...
Solutions to Problems; Chapter 6 349 4.5. k = 86. 4.6. Let u = tan A, v = tan B, w = tanC, and let the fourth root be y. Wehavep ...
350 Answers to Exercises and Solutions to Problems Case4.~=3,u+v=3,sothata=9-a/3~u=27/4.Thecubicis (x - 3)(x2 - (^32) - g/4) = x ...
Solutions to Problems; Chapter (^6 351) = b2 +2d+ac. The sum of all products of three of the zeros is (uw + 2v)(cw + z”) + (uw + ...
352 Answers to Exercises and Solutions to Problems there must be zeros in the other, in order for the imaginary parts to cancel ...
Solutions to Problems; Chapter (^6 353) We have that Cw;’ = 12 - 3x11:~ = 12 - 3(24) = -60, Cw;‘wj’ = 48 - 24Cvf2 + 9(Cv;2v;2) = ...
354 Answers to Exercises and Solutions to Problems Answers to Exercises Chapter 7 1.5. p.(t)= (t -ai)...(tG).+*(t- a,) I (Ui -Ul ...
Answers to Exercises; Chapter 7 355 is a polynomial of degree k, each of its terms can be written as a linear combination of fac ...
356 Answers to Exercises and Solutions to Problems 2.4. (a) Sketch graphs. pi(t) = 0. ps(t) = l/2, since the difference t2 - l/2 ...
Answers to Exercises; Chapter (^7 357) Remark. BUM) = f&(i) ( ; ) C-V-” ( :r,” )tr = gg(-l)p-kf (:) ( ; ) ( ; ) t’ = g (e ) ...
358 Answers to Exercises and Solutions to Problems 3.5. (a) Wi = l/n. (c) WI TJ.. a1 a2 .awn= n a1 w1... a~~~2(a~-lu~)W*-1+W* 5 ...
Solutions to Problems; Chapter 7 359 Equality occurs only when 1 - x = x - y = y - z = z = l/4, so that the only solution is (2, ...
360 Answers to Exercises and Solutions to Problems Since, subject to u + v = 1, uv 5 l/4, it follows that c/a - b/u 2 4(9/2)2 - ...
Solutions to Problems; Chapter 7 361 from which the inequality (*) follows, since 0 < w < 1. Equality occurs C4(u+V)w=v(j( ...
362 Answers to Exercises and Solutions to Problems See Problem 358, Crux Muthemuticorum 4 (1978); 161; 5 (1979), 84. 4.14. First ...
«
14
15
16
17
18
19
20
21
22
23
»
Free download pdf