Can someone help me with this please

2. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and 2-2i.

inna [77]

The polynomial equation for the given roots is x³-7x²+20x-24=0.

Given that, the polynomial equation of the smallest degree whose roots are 3, 2+2i and 2-2i.

Now, we need to write the polynomial equation.

<h3>What is a polynomial equation? </h3>

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation. For an equation to be a polynomial equation, the variable in it should have only non-negative integer exponents. i.e., the exponents of variables should be only non-negative and they should neither be negative nor be fractions.

Now, x=3, x=2+2i and x=2-2i

x-3, x-2-2i and x-2+2i

So, the polynomial equation is (x-3)(x-2-2i)(x-2+2i)=0

⇒(x-3)(x(x-2-2i)-2(x-2-2i)+2i(x-2-2i))=0

⇒(x-3)(x²-2x-2xi-2x+4+4i+2xi-4i-4i²)=0

⇒(x-3)(x²-2x-2x+4-4i²)=0

⇒(x-3)(x²-4x+4+4)=0 (∵i²=-1)

⇒(x-3)(x²-4x+8)=0

⇒x(x²-4x+8)-3(x²-4x+8)=0

⇒x³-4x²+8x-3x²+12x-24=0

⇒x³-7x²+20x-24=0

Therefore, the polynomial equation for the given roots is x³-7x²+20x-24=0.

To learn more about the polynomial equation visit:

brainly.com/question/20630027.

#SPJ1

3 0

2 years ago

Round 60488 to the nearest ten thousand

ANTONII [103]

60,000 would be the answer because it stays the same if under 5 it stays if above 5 rounds up once

4 0

3 years ago

Read 2 more answers

Please help. will give brainliest

vichka [17]

Answer:

B. The probability that the student received a grade better than C is 0.45

Step-by-step explanation:

<u>Total number of students:</u>

15 + 30 + 35 + 16 + 4 = 100

<h3>Statements</h3>

A.

p(<D) = 4/100 = 0.04
0.04 ≠ 0.2
Incorrect

B.

p(>C) = (30 + 15)/100 = 45/100 = 0.45
0.45 = 0.45
Correct

C.

p(not A or B) = (100 - 15 - 30)/100 = 55/100 = 0.55
0.55 ≠ 0.45
Incorrect

D.

p(B or C) = (30 + 35)/100 = 65/100 = 0.65
0.65 ≠ 0.35
Incorrect

6 0

3 years ago

The world population at the beginning of 1980 was 4.5 billion. Assuming that the population continued to grow at the rate of app

AfilCa [17]

Answer:

$Q(t) = 4.5(1.013)^{t}$

The world population at the beginning of 2019 will be of 7.45 billion people.

Step-by-step explanation:

The world population can be modeled by the following equation.

$Q(t) = Q(0)(1+r)^{t}$

In which Q(t) is the population in t years after 1980, in billions, Q(0) is the initial population and r is the growth rate.

The world population at the beginning of 1980 was 4.5 billion. Assuming that the population continued to grow at the rate of approximately 1.3%/year.

This means that $Q(0) = 4.5, r = 0.013$

So

$Q(t) = Q(0)(1+r)^{t}$

$Q(t) = 4.5(1.013)^{t}$

What will the world population be at the beginning of 2019 ?

2019 - 1980 = 39. So this is Q(39).

$Q(t) = 4.5(1.013)^{t}$

$Q(39) = 4.5(1.013)^{39} = 7.45$

The world population at the beginning of 2019 will be of 7.45 billion people.

6 0

3 years ago

Round 38.49 to the nearest whole number

AnnyKZ [126]

38. The nearest whole number to 38.49 is 38 because at .5 you begin rounding up to the nearest whole number.

8 0

3 years ago