MATHEMATICS MIDDLE SCHOOL

What are the real and complex solutions of the polynomial equation? x^3-8=0. with imaginary numbers

Answers

Answer 1

Answer:

Answer: The solutions are : $2, -1 + √(3)i , -1 - √(3)i$

Our equation is $x^(3) - 8 = 0$

and we know that: $8 = 2^(3)$

then we can write our equation as: $x^(3) - 2^(3) = 0$

And using the identity: $a^(3) - b^(3) = (a-b)*(a^(2) +ab+ b^(2) )$

where a = x and b = 2, then our equation is:

$x^(3) - 2^(3) = (x-2)*(x^(2) +2x+ 2^(2) )= 0$

them, if x = 2 the first part is zero, so x = 2 is a solution, and now we need to see the second part in order to find the complex solutions.

$x^(2) + 2x + 4 = 0$

Here we need to use Bhaskara:

if $ax^(2)+ bx + c=0$ for a, b and c constants, then:

x = $\frac{-b +-\sqrt{b^(2) - 4ac } }{2a}$

in our problem we have:

$x = (-2 +-√(4 - 16) )/(2) = -1 +-\sqrt{(4 - 16)/(4) } = -1 +- √(-3) = -1 +-√(3) i$

So here we have two complex solutions: $x = -1 + √(3)i$ and $x = -1 - √(3) i$ .

Answer 2

Answer:

Answer:

Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i

or 2, -1 + 1.58 i and -1 - 1.58i

(where the last 2 are equal to nearest hundredth).

Step-by-step explanation:

The real solution is x = 2:-

x^3 - 8 = 0

x^3 = 8

x = cube root of 8 = 2

Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-

a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Here a = x and b = 2 so we have

(x - 2)(x^2 + 2x + 4) = 0

To find the complex roots we solve x^2 + 2x + 4 = 0:-

Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2

= -1 +/- (sqrt( -10)) / 2

= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i

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What are the roots of the polynomial equation?

x^2 + x -72 =0

Answers

There are many ways you can go. I'm going to start out factoring the whole thing.
(x+9)(x-8) = 0
seperate these into two different equations.
x+9 = 0 and x-8 = 0
x= -9 x=8
Make sure you check it by substituting. Sometimes you might have to reject an answer. In this case you don't. Therefore, 8 and -9 are your roots!

Answer:

Step-by-step explanation:

Make sure you put them in the correct order:

$(4)/(9)$ ×m= 72 what is M?

Answers

Hello lets solve this! :)
$\sf(4)/(9)m = 72\n\n\sf{Multiply~(9)/(4)~on~both~sides~to~isolate~m}\n\n(4)/(9)m * (9)/(4) = 72* (9)/(4)\n\nm = 72* (9)/(4)\n\nm = 18 * 9\n\n\boxed{\bf{m=162}}$

Hope I helped! IIf you have any other questions or would like further explanation just let me know!! :)

(4/9)m=72
m=(72*9)/4
m=648/4
m=162

answer. m=162

What is the value of the 5 in 0.750

Answers

it is in the hundrethds place

8th grade math equation of the line in slope intercept form

Answers

y = 2x.
The slope is 6/3, which simplifies to 2.
the y intercept is 0.

Can you please help me with the sheet??

Answers

1. 25 minutes
2. 41 minutes
3. 21 wheels
4. 7
5. 160
6. 415 miles

Michael had $550 in his savings account. He took out $30.75 every month for one year. What is the net change in Michael’s account balance following these withdrawals?

Answers

The net change in Michael's account balance after withdrawals of $30.75 for 12 months is $181.

What is an arithmetic operation?

The four fundamentaloperations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

From the data given in the question,

Michael has $550 in saving account.

Per month withdrawal by Michael is $30.75

Withdrawal for 12 months = $30.75 × 12 = $369.

Change in Michael's account balance = ($550 - $369) = $181

Therefore, the change will be equal to $181.

To know more about arithmetic operation:

brainly.com/question/13585407

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Answer:

The answer is -$369.00

Step-by-step explanation: