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2 years ago

Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?

Mathematics

2 answers:

svlad2 [7]2 years ago

3 0

Answer:

C. $f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))$

Step-by-step explanation:

We want to find the equation of a polynomial the following properties;

i. Leading coefficient is 1

ii. roots (7 + i) and (5 – i) with multiplicity 1

Recall the complex conjugate properties of the roots of a polynomial.

According to this property, if

$a+bi$ is a root of a polynomial, then the complex conjugate, $a-bi$ is also a root.

This means that:

(7 - i) and (5 + i) with multiplicity 1 are also roots of this polynomial.

The complete set of roots are:

$x=(7+i),x=(7-i),x=(5-i),x=(5+i)$

Therefore the polynomial is:

$f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))$

The correct choice is C.

vovikov84 [41]2 years ago

3 0

Answer:

C. f(x)= (x-(7-i)) (x-(5+i))(x-(7+i))(x-(5-i)

Step-by-step explanation:

edge 2020

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what is 1608 divided by 268, my answer was 5 but apparently its 6 so please explain why and show work :)

Sever21 [200]

If you multiply 268 with 6, you get 1608 as your answer.

6 0

2 years ago

The present age of nitin is two times the present age of his sister pooja. After 7 years their ages will add to 68 years. Find t

svlad2 [7]

N=2p

(n+7) + (p+7) = 68

2p + 7 + p + 7 = 68

3p + 14 = 68

3p = 68 - 14 = 54

p=54/3=18

n=2p=36

Check: (18+7)+(36+7)=25+43=68 good

7 0

1 year ago

1. Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 during

dolphi86 [110]

9514 1404 393

Answer:

$3891.10

Step-by-step explanation:

This question is a bit unusual in that the interest is compounded annually, but payments and withdrawals are made monthly. The effective monthly rate is ...

1.05^(1/12) -1 = 0.407412378% = i

We assume that payments to the annuity are made at the end of the month, and that withdrawals are made at the beginning of the month. (The last payment and the first withdrawal are made on the same day.)

The amount of money required in the fund is ...

A = $4000(1 -(1.00407^-360))/(1 -1.00407^-1) = $757,712.88

The amount of money needed each month to be put into the fund is P, where ...

$757,712.88 = P(1 -1.00407)^(-12(60-28))/(1 -1.00407^-1) = 194.7297P

P = $757,712.88/194.7297 = $3891.10

Yejin needs to save $3891.10 each month to meet her retirement goal.

_____

<em>Sanity check</em>

Yejin wants payments for 30 years from the fund to which she has contributed for 32 years. The similarity of the time periods means that Yejin's monthly contribution will need to be very similar to the amount she plans to withdraw.

The only ways to reduce the required contribution are to earn a higher interest on deposits, or to adjust the relative time periods (retire later).

3 0

1 year ago

Which expression can be used to find the sum of the polynomials? (9 – 3x2) (–8x2 4x 5)

SIZIF [17.4K]

For this case we have:

Polynomial 1: $P (x) = 9-3x ^ 2$

Polynomial 2: $Q (x) = - 8x ^ 2 + 4x + 5$

Sorting the polynomials:

Polynomial 1: $P (x) = - 3x ^ 2 + 9$

Polynomial 2: $Q (x) = - 8x ^ 2 + 4x + 5$

Adding term to term (similar) we have:

$P (x) + Q (x) = (- 3-8) x ^ 2 + (0 + 4) x + (9 + 5)\\P (x) + Q (x) = - 11x ^ 2 + 4x + 14$

Answer:

$A (x) = P (x) + Q (x) = - 11x ^ 2 + 4x + 14$

7 0

1 year ago

Read 2 more answers

Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 + 24x – 35?

QveST [7]

<span>I note that this problem starts out with "Which is a factor of ... " This implies that you were given several answer choices. If that's the case, it's unfortunate that you haven't shared them.

I thought I'd try finding roots of this function using synthetic division. See below:

f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
Please use " ^ " to denote exponentiation. Thanks.

Possible zeros of this poly are factors of 35: plus or minus 1, plus or minus 5, plus or minus 7. Use synthetic division; determine whether or not there is a non-zero remainder in each case. If none of these work, form rational divisors from 35 and 6 and try them: 5/6, 7/6, 1/6, etc.

Provided that you have copied down the function
</span>f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35 properly, this approach will eventually turn up 1 or 2 zeros of this poly. Obviously it'd be much easier if you'd check out the possible answers given you with this problem.

By graphing this function, I found that the graph crosses the x-axis at 7/2. There is another root.

Using synth. div. to check whether or not 7/2 is a root:

___________________________
7/2 / 6 -21 -4 24 -35
21 0 -14 35
----------- ------------------------------
6 0 -4 10 0

Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial. Thus, (x-3.5), or (x-7/2), is a factor.

7 0

1 year ago

Read 2 more answers