426 Cubic Equations in Real Numbers
410 − 7 − 6
###
1###410 − 7 − 6
4##
1###410 − 7 − 6
4##
14##(^410) − 7 − 6
416#
14##
(^410) − 7 − 6
416#
149#
(^410) − 7 − 6
41636
149#
410 − 7 − 6
41636
14930
We’ve failed again! But it’s not a total loss. We’ve learned something. The first “test root” pro-
duced a negative remainder. The second “test root” produced a positive remainder. This tells
us that the number we’re seeking lies between 2 and 4.
We try, we succeed
Let’s see what happens with a “test root” of 3. By now you must be thinking, “A computer
would be a big help with all this.” That’s true, but things are going to work out neatly this
time. We won’t need a computer. Let’s go ahead: