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Oliga [24]
3 years ago
8

Which of the following is a polynomial with roots

Mathematics
2 answers:
PtichkaEL [24]3 years ago
5 0
a(x-x_1)(x-x_2)(x-x_3)\\\\x_1=-\sqrt3;\ x_2=\sqrt3;\ x_3=-2;\ a=1\\\\subtitute\\\\(x+\sqrt3)(x-\sqrt3)(x+2)=(x^2-3)(x+2)\\\\=\boxed{x^3+2x^2-3x-6}\to\fbox{B.}
Anuta_ua [19.1K]3 years ago
5 0
<span> the polynomial has the factor (x-n) </span>
<span>So any polynomial with these roots, must have the factors (x+sqrt(3))(x-sqrt(3))(x+2) </span>
<span>Since these are cubic polynomials (highest x term is x^3), these are all the factors, so the polynomial is of the form: </span>
<span>k(x+sqrt(3))(x-sqrt(3))(x+2) </span>
<span>And since the x^3 term is 1, the constant k must be 1. </span>

<span>So, the polynomial must be the one which is equal to: </span>
<span>(x+sqrt(3))(x-sqrt(3))(x+2) </span>
<span>Since the constant term (the last term) is different for each of your 4 options, you just need to evaluate the constant term and see which one matches. </span>
<span>i.e. the answer is whichever polynomial has a constant term equal to </span>
<span>sqrt(3) times (-sqrt(3)) times 2</span>
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A manufacturer claims that fewer than 6% of its fax machines are defective. to test this claim, he selects a random sample of 97
AfilCa [17]

Let P be the population proportion, p be the sample proportion, n be the sample size.

A manufacturer claims that fewer than 6% of its fax machines are defective. It means P=0.06

Sample size n=97 and sample proportion p=0.05

The hypothesis to be tested is

H0: P ≥ 0.06 V/s Ha: P < 0.06

Here the hypothesis for testing population proportion we use z test statistics. Z test statistics is give by

Z = \frac{p -p_{0}}{\sqrt{p_{0}(1-p_{0})/n}}

Where p =sample proportion = 0.05

p0 = hypothesized proportion value =0.06

Using given values into test statistics we get

Z = \frac{0.05 -0.06}{\sqrt{0.06(1-0.06)/97}}

Z = -0.41

The p-value for left tailed alternative hypothesis is given by

P-value = P(z < z cal)

where zcal = Z test statistics value

Here zcal = -0.41

P-value = P(Z < -0.41)

Using z score table to find probability below z=-0.41

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P-value for testing the given claim is 0.3409

3 0
3 years ago
if 40 percent of a circle is taken what would be the angle you would draw to represent 40 percent of the circle
Tema [17]
If you mean 40% of the circle with the rotation at the center of the circle, then you do this:
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6 0
3 years ago
Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C. (-4,8). (-5, -6)
konstantin123 [22]

Answer:

y2-y1/x2-x1

Step-by-step explanation:

x1= -4        x2= -5

y1= 8          y2= -6

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so M = 14

y-y1=m(x-x1)

y-8=14(x+4)

8y=14x+56

rearrange

-14x+8y=56

but you need it in the form of AX+BX=C (THE X SHOULD BE POSITIVE SO CHNAGE ALL THE SIGNS )

14X-8Y=-56

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3 years ago
According to records from the last 50 years, there is a 2/3 chance of June temperatures being above 80 F. Azul needs to find the
umka21 [38]
I think the answer is 52% because I got it correct on i-Ready. I really hope this helps because I hate that when you fail you have to redo a lesson. 

Have a great day and let me know if this is the right answer. 
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matrenka [14]

Answer:

31

Step-by-step explanation:

 

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