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Misha Larkins [42]
3 years ago
13

Use the given zero to find the remaining complex zeros of the polynomial function and write the polynomial as a product of linea

r factors.
f(x)=x^3+8x^2+6x-52; zero:2
Mathematics
1 answer:
lidiya [134]3 years ago
5 0

Answer:

(x - 2)(x - 5 + 2i)(x - 5 - 2i)

Step-by-step explanation:

If one zero is 2, then one factor is (x - 2).

Use synthetic division here.  Taking the coefficients 1, 8, 6 and -52, divide 2 into them:

2    /  1      8      6     -52

                2     20     52

      -----------------------------

          1     10     26     0

Because the remainder is zero, we know that 2 is a root and (x - 2) is a factor, and that the coefficients of the quadratic quotient are 1, 10 and 26.

The discriminant is thus b^2 - 4ac, or 10^2 - 4(1)(26), or  100 - 104, or -4.

Because the discriminant is negative, we know that there will be two factors which themselves are complex conjugates.  One such factor is

      10 ± √-4         10 ± 2i

x = --------------- = ---------------

             2                   2

The complex zeros are thus x = 5 ± 2i.

The corresponding factors are (x - 5 + 2i) and (x - 5 - 2i)

and so the polynomial is

(x - 2)(x - 5 + 2i)(x - 5 - 2i)

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Compare the surface area-to-volume ratios of the moon and mars. express your answer using two significant figures.
antoniya [11.8K]

we know that

For a spherical planet of radius r, the volume V and the surface area SA is equal to

V=\frac{4}{3} *\pi *r^{3} \\ \\ SA=4*\pi *r^{2}

The
ratio of these two quantities may be written as

SAV =\frac{(4*\pi*r^{2})}{(\frac{4}{3}*\pi*r^{3})}     \\  \\ SAV =\frac{3}{r}

we know

rMoon=1,738Km\\ rMars=3,397 Km

\frac{SAV Moon}{SAV Mars} =\frac{3}{rMoon} *\frac{rMars}{3} \\ \\ \frac{SAV Moon}{SAV Mars} =\frac{rMars}{rMoon} \\ \\ \frac{SAV Moon}{SAV Mars} =\frac{3,397}{1,738} \\ \\ \frac{SAV Moon}{SAV Mars} =1.9545

therefore

the answer is

1.9

5 0
3 years ago
Read 2 more answers
PLEASE SOLVE CORRECTLY!!! I HAVE CHECKED THE ANSWER AND IT SAYS $64.67 BUT I DON'T KNOW THE PROCESS TO GET THAT ANSWER!!! HELP!!
Sphinxa [80]

Answer:

see below

Step-by-step explanation:

First determine how much is subtracted from the account

12.57+24.95+36.86 =74.38

They charge .15 per check=3*.15 = .45

Subtract the amounts of the checks and the check fees

139.50-74.38-.45 =64.67

7 0
3 years ago
Read 2 more answers
#19 please I’m literally failing math
ankoles [38]

Answer:

$51.12

Step-by-step explanation:

Hello there!

In number 19, we want to find the total price of a sweatshirt that costs $48 dollars but has 6.5% sales tax

Sales tax is a small percentage of the cost of an item that is added to items when they are being sold.

In this problem, 6.5% of the cost of the sweatshirt will be added to the cost of the sweatshirt in the form of sales tax. The price of the sweatshirt plus the amount in sales tax will be the total cost of the sweatshirt.

Translating that as an equation,

48 + 48*6.5%=total cost

You can calculate 48*6.5% as \frac{48*6.5}{100}, which is equal to 3.12

So that means that $3.12 will be added to the cost of the sweatshirt.

Therefore,

48 + 3.12=<u>$51.12</u>, which will be the total cost of the sweatshirt, including sales tax

Hope this helps!

7 0
2 years ago
How to do system of equations
aliya0001 [1]

Answer: The three methods most commonly used to solve systems of equation are substitution, elimination and augmented matrices.

Step-by-step explanation:

Substitution is a method of solving systems of equations by removing all but one of the variables in one of the equations and then solving that equation.

Elimination is another way to solve systems of equations by rewriting one of the equations in terms of only one variable. The elimination method achieves this by adding or subtracting equations from each other in order to cancel out one of the variables.

Augmented matrices can also be used to solve systems of equations. The augmented matrix consists of rows for each equation, columns for each variable, and an augmented column that contains the constant term on the other side of the equation.

7 0
3 years ago
There is a geometrical relation that arc of circle is equal to the central angle.
miss Akunina [59]
The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That's why radians are natural: a central angle of one radian will span an arc exactly one radius long.
Is the correct
6 0
3 years ago
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