An introduction to the modern theory of equations, by Florian Cajori.

ANSWERS

~ 6, Ex. 4: 47112.
Ex. 5: - 252493.
Ex. 6: (1 +/-29).
~14, Ex. 3: -, ~ V5.
Ex. 4: - ~, -1 ~ /V2.
Ex. 5: -2-, -5, -5.
Ex. 6: 2,, -3, -3.
~ 15, Ex. 2: a2 - 2 b.
Ex. 6: c -ab.
Ex. 7: 2 - 2 b.
Ex. 8: 3 c - ab.
Ex. 9: b2 2 ac+ 2 d.
Ex.12: -- 1 —s'
~ 21, Ex. 4: -1 triple, 5 double.
~29, Ex. 7: x4-60 x2 - 700 -
100 = 0.
Ex. 8: x4 - 3 3+ 768 X +
1024 = 0.
~ 31, Ex. 3: am -=0.
Ex. 6: c, 1, -- b b-42
2 a
~ 34, Ex. 1: H= -, G - 12.
Ex. 2: H=- -50, = -135,
= - 59.
~35, Ex. 5: 3 - 42 z2+ 441 z +
1388 = 0.
~ 37, Ex. 2: Two of the roots of I
are equal, or the three are
in arithmetical progression.
Ex. 3: -2376.
Ex. 4: 0.

~39, Ex. 2: (1) 41, 12.
(2) 41, 11.
(3) 37, 7.
(4) 31, 31.
~41, Ex. 3: (1) 51 and —5.
(2) 4 and -.
(3) 12 and -.
~ 42, Ex. 3: (1) Between 8 and 9,
- 1 and - 2, - 4 and - 5.
(2) Between 3 and 4,
4 and 5, - 4 and
- 5, -5 and -6.
(3) Between 1 and 2,
2.and 3, 5 and 6,
6 and 7.
~ 44, Ex. 2: 156, 31.
~ 49, Ex. 5: (1) two real 2.+, -

2. +

~ 50, Ex. 1:
289,
~ 56, Ex. 1:

(2) 3.21, 3.22, - 17.4.
(3) three real.
H=9I, G=25, I=
J=- 940, D = +.
(1) 1.35759..
(2) -1.53172..
(3).885119..
- 1.46057..
(4) 1.3518..
(5) 1.51851..
-.50849..
- 1.24359..

~ 67, Ex. 1: - 1,-2 ~ -~ V-3,~i

235