Find all the zeros of the polynomial function. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by agraphing utility as an aid in obtaining the first zero.fx)-x-3x-13x + 15The zeros of the function are(Use a comma to separate your answers as needed.)Enter your answer in the answer box.Pre to searchhpHEW LETT PAC KAR Dinsprt schome12deletef1110f8f4&7$4%5backspaceOlock963}UTERhomeenterLKHFDGpauseTshiftMVBCctrlalt00

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Asked Aug 8, 2019
Find all the zeros of the polynomial function. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a
graphing utility as an aid in obtaining the first zero.
fx)-x-3x-13x + 15
The zeros of the function are
(Use a comma to separate your answers as needed.)
Enter your answer in the answer box.
P
re to search
hp
HEW LETT PAC KAR D
ins
prt sc
home
12
delete
f11
10
f8
f4
&
7
$
4
%
5
backspace
O
lock
9
6
3
}
U
T
E
R
home
enter
L
K
H
F
D
G
pause
Tshift
M
V
B
C
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Find all the zeros of the polynomial function. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero. fx)-x-3x-13x + 15 The zeros of the function are (Use a comma to separate your answers as needed.) Enter your answer in the answer box. P re to search hp HEW LETT PAC KAR D ins prt sc home 12 delete f11 10 f8 f4 & 7 $ 4 % 5 backspace O lock 9 6 3 } U T E R home enter L K H F D G pause Tshift M V B C ctrl alt 00

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check_circleExpert Solution
Step 1

Given information:

The given polynomial function is  

f(x)x332-13x +15
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f(x)x332-13x +15

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Step 2

Given information:

The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number.

So, the coefficients are 1,-3,-13,15.

There are 2 changes.

This means that there are 2 or 0 positive real roots.

To find the number of negative real roots, substitute x with -x in the given polynomial: 

f(-x)=(x3-3(-x)2-13(-x)+15
=-x3-3x2 +13x+15
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f(-x)=(x3-3(-x)2-13(-x)+15 =-x3-3x2 +13x+15

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Step 3

The coefficients are -1,-3,13,15.

There is 1 change.

This means that there is 1 negat...

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