= xtraor- ld be engendered by imaginary numbers. From this time of their mystical character, although their full acceptance the roots of the cubic x in the 1800s. 1 36r2= 20x + 56. (c) 3 (d) x64 6x2+ 24x. 2. Derive Cardan's formula p'3 + 27 q2 V 4 3q 3q V 4 2 2 27 for solving the cubic equation x3 p>O and q> 0. = px +q, where 12 3. Using Cardan's formula, obtain one root of each of the ++ Cardan's Ars Magna following cubic equations. HIB (a) x3+24x 16. (b) x315x6x218 (c) x327 (d) x39x 12. 6x2+15x +8 3x2+27x+ 41. AN 6x2+58. . AR (e) x3 = (f) x3= 4. Solve the cubic equation x+6x2+x =14. Problems 5-11 appear in Cardan's Ars Magna. 5. Chapter 5, Problem 2. There were two leaders, each whom divided 48 aurei among his soldiers. One of these had two more soldiers than the other. The one who had two soldiers fewer had four aurei more for each soldier. Find how many soldiers each had. 6.Chapter 37, Problem 1. The dowry of Francis's wife 100 more than Francis's own property is worth quare of the dou aurei and the than the 100 nore SS

= xtraor- ld be engendered by imaginary numbers. From this time of their mystical character, although their full acceptance the roots of the cubic x in the 1800s. 1 36r2= 20x + 56. (c) 3 (d) x64 6x2+ 24x. 2. Derive Cardan's formula p'3 + 27 q2 V 4 3q 3q V 4 2 2 27 for solving the cubic equation x3 p>O and q> 0. = px +q, where 12 3. Using Cardan's formula, obtain one root of each of the ++ Cardan's Ars Magna following cubic equations. HIB (a) x3+24x 16. (b) x315x6x218 (c) x327 (d) x39x 12. 6x2+15x +8 3x2+27x+ 41. AN 6x2+58. . AR (e) x3 = (f) x3= 4. Solve the cubic equation x+6x2+x =14. Problems 5-11 appear in Cardan's Ars Magna. 5. Chapter 5, Problem 2. There were two leaders, each whom divided 48 aurei among his soldiers. One of these had two more soldiers than the other. The one who had two soldiers fewer had four aurei more for each soldier. Find how many soldiers each had. 6.Chapter 37, Problem 1. The dowry of Francis's wife 100 more than Francis's own property is worth quare of the dou aurei and the than the 100 nore SS

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Description: #3 a and b =xtraor-ld be engendered by imaginary numbers. From this timeof their mystical character, although their full acceptancethe roots of the cubic xin the 1800s.136r2= 20x + 56.(c)3(d) x64 6x2+ 24x.2. Derive Cardan's formulap'3+27q2V 43q3qV 42

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.3: Quadratic Equations

Problem 82E

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Topic Video

Question

#3 a and b

=
xtraor-
ld be engendered by imaginary numbers. From this time
of their mystical character, although their full acceptance
the roots of the cubic x
in the 1800s.
1
36r2= 20x + 56.
(c)
3
(d) x64 6x2+ 24x.
2. Derive Cardan's formula
p'3
+
27
q2
V 4
3q
3q
V 4
2
2
27
for solving the cubic equation x3
p>O and q> 0.
= px +q, where
12
3. Using Cardan's formula, obtain one root of each of the
++

Cardan's Ars Magna
following cubic equations.
HIB
(a) x3+24x 16.
(b) x315x6x218
(c) x327
(d) x39x 12.
6x2+15x +8
3x2+27x+ 41.
AN
6x2+58.
.
AR
(e) x3 =
(f) x3=
4. Solve the cubic equation x+6x2+x =14.
Problems 5-11 appear in Cardan's Ars Magna.
5. Chapter 5, Problem 2. There were two leaders, each
whom divided 48 aurei among his soldiers. One of
these had two more soldiers than the other. The one
who had two soldiers fewer had four aurei more for
each soldier. Find how many soldiers each had.
6.Chapter 37, Problem 1. The dowry of Francis's wife
100
more than Francis's own property is worth
quare of the dou
aurei
and the
than the
100
nore
SS

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