All categories

3 years ago

Can someone help me solve this? Thanks!

Mathematics

1 answer:

netineya [11]3 years ago

5 0

9514 1404 393

Answer:

p(x) = x³ -3x²+4x -2

Step-by-step explanation:

When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.

Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...

p(x) = (x -1)(x -(1+i))(x -(1-i))

The last two factors can be recognized as the factors of the difference of squares:

((x -1) +i)((x -1) -i) = (x -1)² -i²

= (x² -2x +1) -(-1) = x² -2x +2

Now the whole polynomial can be seen to be ...

p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)

p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses

p(x) = x³ -3x²+4x -2

You might be interested in

During the 7th examination of the Offspring cohort in the Framingham Heart Study, there were 1219 participants being treated for

AlexFokin [52]

Answer:

95% confidence interval for the proportion of the population which are on treatment is [0.3293 , 0.3607].

Step-by-step explanation:

We are given that during the 7th examination of the Offspring cohort in the Framing ham Heart Study, there were 1219 participants being treated for hypertension and 2,313 who were not on treatment.

The sample proportion is : $\hat p$ = x/n = 1219/3532 = 0.345

Firstly, the pivotal quantity for 95% confidence interval for the proportion of the population is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion = 0.345

n = sample of participants = 3532

p = population proportion

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level of

significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

<u>95% confidence interval for p</u>= [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.345-1.96 \times {\sqrt{\frac{0.345(1-0.345)}{3532} } }$ , $0.345+1.96 \times {\sqrt{\frac{0.345(1-0.345)}{3532} } }$ ]

= [0.3293 , 0.3607]

Hence, 95% confidence interval for the proportion of the population which are on treatment is [0.3293 , 0.3607].

6 0

3 years ago

20 minutes for $3.75 or 35 minutes for $5.25. Whats the better deal

Murrr4er [49]

35 minutes for 5.25$

5 0

3 years ago

Read 2 more answers

the larger of two positive numbers is 5 more then the smaller. The product of the numbers is 66. find the numbers

Serjik [45]

Answer: 30.5 and 35.5

Step-by-step explanation:

We can use a system of linear equations to find out the answer to this problem. The larger number will be x and the smaller number will be y.

x=y+5

x+y=66

Substitute y+5 in for the bottom equation to get y+5+y=66. Simplify to get 2y+5=66. Subtract 5 from both sides and get 2y=61. Divide by 2 to get y=30.5. This is the smaller number. Add 5 to get the bigger number, which is 35.5

7 0

3 years ago

A.X B.Y C.Z D.C really need help with this one not really sure about the answer

Scrat [10]

Angle B corresponds to angle Y

8 0

3 years ago

Read 2 more answers

Mr. Chang wants to retire in 10 years. He deposits $650.00 every three months into his retirement investment account. If the acc

Fittoniya [83]

Answer:

Mr. Chang will have 15714.90 dollars.