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We have a problem here......we can't have a polynomial with only one complex root....all complex roots to a polymomial occur in pairs. Specifically, in your polynomial, the other complex root would be 2 + 3i.

I'll construct one with all these roots, and you can take your chances.   So we have....

(x + 1)(x + 1)(x -(2-3i))(x - (2 + 3i))

This gets a little messy, so hang on...multiplying the first two terms together, we get  x^2 + 2x + 1

Let's set this aside for the moment and concentrate on the last two .... so we have

(x -(2-3i))(x - (2 + 3i)) = (x^2 -x (2 - 3 i) - x (2 + 3i) + (2-3i)(2+3i) =

(x^2 -2x +3xi -2x -3xi + 4 -6i + 6i - 9(i)^2) = (x^2 - 4x + 4 + 9) = (x^2 - 4x + 13)

Now, putting the two together, we have

(x^2 + 2x + 1) (x^2 - 4x +13) =

x^4 + 2x^3 + x^2 - 4x^3 - 8x^2 - 4x + 13x^2 +26x + 13 =

x^4 -2x^3 + 6x^2 + 22x + 13 = P(x)

See...I told you it could get messy....!!

BTW...I checked this one with a solver and it was correct.......

When logs are used in addition, they can also be written as multiplication. You can combine these logs in the form  of multiplication.

You should rewrite the coeffecient of 20 as an exponent in both logs.

37 + (log6000^20) + (log30^20)

Rewrite in the form of multiplication. Keep the log and mulitiply the numbers of the log.

37 + log(6,000*30)^40      The exponents were added, because of multiplication.

37 + log180,0000^40

Thanks for clarifying, I took it that "the number" on the left was 2x; and so in the right side of the equation, inside the parenthesis, "the number" 2x is subtracted by 5 and then it is mulitiplied by 8.

But I see now, thanks!

B=P(1+r)exponent n

B=balance

P=principal or the starting amount

r=intrest rate %

n= number of payments

B=70000(1+.09)exponent 9

In the manner you have it written, we have... (x^2) / 3

This says to square x and then divide by three.  So we have

(2)^2 / 3  =  4 / 3    And that's your answer      ....However.......

If you meant this,  x^(2/3), we have something different

This says to "square" x and then take the cube root of that answer

So we have 2^2 = 4

And the cube root of 4 can be written as (4)^(1/3) ≈ 1.59

Note that this brings up an important point......the placement of parentheses matter !!!! 

Hope that helped you

Look here

http://web2.0calc.com/questions/how-do-i-type-in-fractions

Wednesday14th May

Polar co-ordinates

0.0275 or 11/400

Oh, dear sir, you are making me shake in my space boots.  

To eat Pi?

1/36 is your answer

5.4

Umm... Does what equal 60?

Look here

http://web2.0calc.com/questions/how-do-i-type-in-fractions

The question, as I interpreted it, is that 8 is being added to the number produced by doubling x

So doubling x  gives us  2x

And adding 8 to it gives

2x + 8

Substituting 8 into the problem, we get

2(8) + 8 = 8(8 -  5)

16 + 8 = 8(3)

24 = 24

That's all I've got !!!

We need to know how many marbles we're drawing out of the bag....one??....two??......three??

What I meant to say/ask was, why isn't 2x inside the parenthesis, because if it is then 8 doesn't work in the equation.

Cphil, when you plug 8 back into the equation as x, it doesn't check out to be true.

OK.....so we have

2x + 8 = 8(x - 5)   And expanding gives

2x + 8 = 8x - 40   Subtract 8x from both sides and 8 from both sides

-6x =-48               Divide both sides by -6             

x = 8

$${\mathtt{20\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1.09}}\right)}^{{\mathtt{10}}} = {\mathtt{47\,347.273\: \!491\: \!842\: \!344\: \!680\: \!2}}$$

≈  $47347.27

Because you are only taking a part of it away. Think of one as something as a whole. It can be a pie, person, whatever. If you take a slice of that pie, you will still have some left; it will just be a smaller amount. If you take a piece of one, it will  be a decimal.

The answer is 78125

I would join becuase this seems like a fun and educational website, and also this is the fourth time you have suggested it, but some of the terms of agreement seem a bit harsh.

your smarter than that, come on it is easy

5*5*5*5*5*5*5= 5 to the seventh power