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Naddik [55]
3 years ago
7

P(x)= x^5-4x^4+3x^3+2x-6 Use Descartes rule of signs to analyze the zeros

Mathematics
1 answer:
maxonik [38]3 years ago
8 0
\bf \begin{array}{cccccccccccllll}
P(x)= x^5&-&4x^4&+&3x^3&+&2x&-&6\\
&yes&&yes&&\textit{no}&&yes
\\\\\\
P(-x)= -x^5&-&4x^4&-&3x^3&-&2x&-&6\\
&\textit{no}&&\textit{no}&&\textit{no}&&\textit{no}
\end{array}

notice where how many "yes" sign change happen in the positive "x"
and the on the negative "-x"

for the P(x) is 3 changes, thus
so is either 3 real positive ones, or 3-2 = 1 real positive one

P(-x) gives no sign changes, so there are 0 negative ones

the polynomial has a degree of 5, thus 5 roots
if it has 3 real positive ones, then it has 2 complex ones
the complex ones pick up the slack per se

if it has 1 real positive one, then it has 4 complex ones

bear in mind complex ones always come in pairs


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Can someone please help me with this geometry homework?
Leno4ka [110]

The distances between the two points, in units, are given as follows:

7. \sqrt{2}

8. 2\sqrt{17}

9. 3\sqrt{2}

10. 3\sqrt{5}

The midpoints are given as follows:

11. (7,-4.5).

12. (2,4).

13. (7,0.5).

14. (5.5,-1.5).

<h3>What is the distance between two points?</h3>

Suppose that we have two points, (x_1,y_1) and (x_2,y_2). The distance between them is given by:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

For item 7, the points are (-3,-2) and (-4,-3), hence the distance is:

D = \sqrt{(-4 + 3)^2 + (-3 + 2)^2} = \sqrt{2}

For item 8, the points are (-3,1) and (5,3), hence the distance is:

D = \sqrt{(5 + 3)^2 + (3 - 1)^2} = \sqrt{68} = 2\sqrt{17}

For item 9, the points are (-3,0) and (0,-3), hence the distance is:

D = \sqrt{(0 + 3)^2 + (-3 - 0)^2} = \sqrt{18} = 3\sqrt{2}

For item 10, the points are (1,-2) and (4,4), hence the distance is:

D = \sqrt{(4 - 1)^2 + (4 + 2)^2} = \sqrt{45} = 3\sqrt{5}

<h3>What is the midpoint concept?</h3>

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

Hence, for item 11, the midpoint is given by:

[0.5(9 + 5), 0.5(1-10)] = (7,-4.5).

For item 12, the midpoint is given by:

[0.5(-5 + 9), 0.5(7 + 1)] = (2,4).

For item 13, the midpoint is given by:

[0.5(9 + 5), 0.5(9 - 8)] = (7,0.5).

For item 14, the midpoint is given by:

[0.5(10 + 1), 0.5(4 - 7)] = (5.5,-1.5).

More can be learned about the distance between two points at brainly.com/question/18345417

#SPJ1

8 0
2 years ago
What do you call the answer?
Marina86 [1]
Something you have said to a question
4 0
4 years ago
Which of these number(s) below are potential roots of the function p(x)=x^4+22x^2-16x-12
Alex Ar [27]

There's no list so we'll generate our own. Technically we're after zeros of p(x), which are the roots of p(x)=0.


The rational zeros are always fractions with a factor of the constant in the numerator and of the leading term in the denominator. Here we have a monic polynomial, leading coefficient 1, so the rational roots are all integers, factors of -12.


The potential rational zeros are: -12, -6, -3, -2, -1, 1, 2, 3, 6, 12



3 0
3 years ago
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irakobra [83]

Answer:

568 square ft.

Step-by-step explanation:

11x24=264

19x16=304

264+304=568

8 0
2 years ago
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Find x and y by Elimination using Multiplication<br> 3x - 4y = -4<br> x + 3y = -10
Ahat [919]
So i think that this is x=7 I think I'm right but not for sure
hope this helps
3 0
3 years ago
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