Solve each polynomial equation in the complex numbers. 2x4−25x3+105x2−115x−87=0 Find the complex zeros of f. x=?
Solve each polynomial equation in the complex numbers. 2x4−25x3+105x2−115x−87=0 Find the complex zeros of f. x=?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
11.Solve each polynomial equation in the
2x4−25x3+105x2−115x−87=0
Find the complex zeros of f.
x=?
(Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
12.Form a third-degree polynomial function with real coefficients, with leading coefficient 1, such that
−8+i and 3 are zeros.
f(x)=?
(Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.)
13.Form a polynomial f(x) with real coefficients, with leading coefficient 1, having the given degree and zeros.
Degree 4; zeros: 3+3i and 3 of multiplicity 2 Enter the polynomial.
f(x)=?
(Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.)
14. Form a fifth-degree polynomial function with real coefficients such that
3i, 1−2i, and 3 are zeros and f(0)=−405.
f(x)=?
(Simplify your answer. Type an expression using x as the variable.)
15.
xy(4,0)(0,-4)
A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 2 and a vertical y-axis labeled from negative 8 to 4 in increments of 2. From left to right, a curve rises at a decreasing rate passing through the labeled plotted point (0, negative 4), and then rises at an increasing rate passing through the labeled plotted point (4, 0).
Form the third-degree polynomial function, f(x), with real coefficients sketched here given that
5i is a zero.
f(x)= ?
(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an expression using x as the variable.)
16.
A.
B.
C.
D.
E.
F.
Use the intermediate value theorem to show that the polynomial
f(x)=x3+2x−5
has a real zero on the interval
[1,2].
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
The polynomial has a real zero on the given interval, because
variation(s) in sign.
f(−x)
has ?variation(s) in sign.
The polynomial has a real zero on the given interval, because
f(1)=?
and
f(2)=?
are opposite in sign.The polynomial has a real zero on the given interval, because
f(1)=?
and
f(2)=?
are outside of the interval.The polynomial has a real zero on the given interval, because
f(1)=?
and
f(2)=?
are complex conjugates.The polynomial has a real zero on the given interval, because
f(1)=?
and
f(2)=?
are both negative.The polynomial has a real zero on the given interval, because
f(1)=?
and
f(2)=?
are both positive.17.Use the intermediate value theorem to find the real zero of the given polynomial correct to two decimal places.
f(x)=x3+2x−6
The real zero correct to two decimal places is ?
(Round the final answer to two decimal places as needed. Round all intermediate values to four decimal places as needed.)
18.
Determine the end behavior, plot the y-intercept, find and plot all real zeros, and plot at least one test value between each intercept. Then connect the points with a smooth curve.
f(x)=x3+2x2−15x−36
Choose the correct end behavior for f(x).
The ends of the graph will extend in the same direction, because the degree of the polynomial is even.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is even.
The ends of the graph will extend in the same direction, because the degree of the polynomial is odd.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is odd.
19.Determine the end behavior, plot the y-intercept, find and plot all real zeros, and plot at least one test value between each intercept. Then connect the points with a smooth curve.
f(x)=2x3+5x2−23x+10
Choose the correct end behavior for f(x).
The ends of the graph will extend in the same direction, because the degree of the polynomial is odd.
The ends of the graph will extend in the same direction, because the degree of the polynomial is even.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is odd.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is even
20.Determine the end behavior, plot the y-intercept, find and plot all real zeros, and plot at least one test value between each intercept. Then connect the points with a smooth curve.
f(x)=7x4−58x3+60x2+250x+125
Choose the correct end behavior for f(x).
The ends of the graph will extend in the same direction, because the degree of the polynomial is odd.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is even.
The ends of the graph will extend in the same direction, because the degree of the polynomial is even.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is odd.
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