Question

Verify that the equation does not have any rational number solutions.

x^{4} − x^{3} − 8x^{2} − 2x + 1 = 0

Find all possible rational roots. (Enter your answers as a comma-separated list.)

Answer #1

Find all solutions of the equation. (Enter all answers including
repetitions. Enter your answers as a comma-separated list.)
x4 + 5x3− 17x2− 15x
+ 42 = 0
Find all solutions of the equation. (Enter
all
answers including repetitions. Enter your
answers as a comma-separated list.)
6x5 + 43x4 + 37x3 − 30x2 = 0
Find all solutions of the equation. (Enter
all answers including repetitions. Enter your answers as a
comma-separated list.)
x3 − 8x2 − 19x − 10...

A grain silo consists of a cylindrical main section and a
hemispherical roof. If the total volume of the silo (including the
part inside the roof section) is 11,000 ft3 and the
cylindrical part is 30 ft tall, what is the radius of the silo,
correct to the nearest tenth of a foot?
r = ft
The real solutions of the given equation are rational. List all
possible rational roots using the Rational Zeros Theorem. (Enter
your answers as a comma-separated...

Use Newton's method with the specified initial approximation
x1 to find x3, the third
approximation to the root of the given equation.
x3 + 5x − 2 =
0, x1 = 2
Step 1
If
f(x) =
x3 + 5x − 2,
then
f'(x) = _____ x^2 + _____
2- Use Newton's method to find all roots of the
equation correct to six decimal places. (Enter your answers as a
comma-separated list.)
x4 = 5 + x
.

1. Find all rational zeros of the polynomial, and then find the
irrational zeros, if any. Whenever appropriate, use the Rational
Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule
of Signs, the Quadratic Formula, or other factoring techniques.
(Enter your answers as comma-separated lists. Enter all answers
including repetitions. If an answer does not exist, enter DNE.)
P(x) = 2x4 + 7x3 − 6x2 − 7x + 4 rational zeros x = irrational zeros
x =
2. A...

Find the number of solutions to
x1+x2+x3+x4=16 with
integers x1 ,x2, x3, x4
satisfying
(a) xj ≥ 0, j = 1, 2, 3, 4;
(b) x1 ≥ 2, x2 ≥ 3, x3 ≥ −3,
and x4 ≥ 1;
(c) 0 ≤ xj ≤ 6, j = 1, 2, 3, 4

2. Find the number of integer solutions to x1 + x2 + x3 + x4 +
x5 = 50, x1 ≥ −3, x2 ≥ 0, x3 ≥ 4, x4 ≥ 2, x5 ≥ 12.

A graphing calculator is recommended. Use Newton's method to
find all solutions of the equation correct to eight decimal places.
Start by drawing a graph to find initial approximations. (Enter
your answers as a comma-separated list.) -2x^7-4x^4+9x^3+2=0

Given the third order homogeneous constant coefficient equation
y′′′+4y′′+y′−26y=0
1) the auxiliary equation is ar3+br2+cr+d= ? =0.
2) The roots of the auxiliary equation are ? (enter answers as a
comma separated list).
3) A fundamental set of solutions is (Enter the fundamental set
as a commas separated list y1,y2,y3)

A graphing calculator is recommended.
Use Newton's method to find all solutions of the equation correct
to eight decimal places. Start by drawing a graph to find initial
approximations. (Enter your answers as a comma-separated list.)
−2x7 − 5x4 + 9x3 + 2 = 0

A graphing calculator is recommended.
Use Newton's method to find all solutions of the equation
correct to eight decimal places. Start by drawing a graph to find
initial approximations. (Enter your answers as a comma-separated
list.)
−3x7 − 5x4 + 9x3 + 7 = 0
x =

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