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I just want to know how

How do you take down a post

yep thanks but please do not post solutions just help

Thanks for the help guys!

**thedarktiger**- Replies: 4

1) Let S be the sum of a finite geometric series with negative common ratio whose first and last terms are 1 and 4, respectively. (For example, one such series is 1-2+4, whose sum is 3.)

There is a real number L such that S must be greater than L, but we can make S as close as we wish to L by choosing the number of terms in the series appropriately. Determine L.

2)If a/b rounded to the nearest trillionth is 0.008012018027, where a and b are positive integers, what is the smallest possible value of a+b?/

**thedarktiger**- Replies: 6

heres the problem

(a)Determine all nonnegative integers r such that it is possible for an infinite arithmetic sequence to contain exactly r terms that are integers. Prove your answer.

seems like an awefull lot of cases

(b)Determine all nonnegative integers r such that it is possible for an infinite geometric sequence to contain exactly r terms that are integers. Prove your answer.

same thing

Why does one root have to be real when the coefficients are?

**thedarktiger**- Replies: 4

Let x, y, and z be complex (i.e., real or nonreal) numbers such that x+y+z, xy+xz+yz, and xyz are all positive real numbers.

Is it necessarily true that x, y, and z are all real, and positive? If so, prove it. If not, give a counterexample.

Thanks. I can prove that they are positive if they are real numbers, but don't see the approach for if they are complex.

The answer for q1 was 14. Interesting.

That means the poly was 2x^3+14x^2-82x+66.

q2 was 86 then.

Thank you for your help.

**thedarktiger**- Replies: 4

These are driving me mad:

(1)Suppose the polynomial

has integer coefficients, and its roots are distinct integers.Given that a_n=2 and a_0=66, what is the least possible value of

?(2)Two of the roots of the polynomial

have product -32.Determine k.

(3)Let

be the roots of f(x).Compute

I just got another similar problem I thought was really cool:

Let r, s, and t be roots of the equation

.Compute

rs/t+st/r+tr/s = ((rs+st+tr)^2-2rst(r+s+t))/rst = (6^2-2*9*(-5))/9 = -6

but strangly, -6 = -(rs+st+rt)...

I dont see how that works

I just thought that was a really cool factorization.

so that can also be

(b^2+2ac)/c = a

maybe I discovered something new. Duno

@Agnishom, on your before last post, you said the answer to (a) is the coefficient of x divided by that of x^4. Thats seven, and its incorrect... I think the answer is -7

Thanks both of you

**thedarktiger**- Replies: 8

For math class homework, I have several problems like this and I don't really know how to do these:

Let g(x) = x^4-5x^3+2x^2+7x-11, and let the roots of g(x) be p, q, r, and s.

(a) Compute pqr + pqs + prs + qrs.

(b) Compute

(c) Compute p^2 + q^2 + r^2 + s^2.

(d) Compute p^2qrs + pq^2rs + pqr^2s + pqrs^2.

Can you help me understand the method, not just do them for me?

Thanks!

Thanks!

**thedarktiger**- Replies: 8

(a) Give an example of two irrational numbers which, when added, produce a rational number. (sqrt(2) and -sqrt(2) )

Now let's consider just the addition of radicals.

(b) Suppose that a and b are positive integers such that both

are irrational. For what values of a and b is rational? Prove your answer.(c) Again assuming a and b positive integers such that both

are irrational, for what values of a and b is rational? Prove your answer.Thank you. I'm stumped!

sorry, I was just really tired and not thinking.

**thedarktiger**- Replies: 3

Let x=a and x=b be the roots of the equation x^2 - mx + 2 = 0.

Suppose that x=a+\frac 1b and x=b+\frac 1a are the roots of the equation x^2 - px + q = 0.

Determine the value of q.

**thedarktiger**- Replies: 1

Let a,b be real numbers such that 0<b <= a.

Prove that the equation x^2+ax-b=0 cannot have two integer roots.

thank you @Olinguito and @bob bundy

**thedarktiger**- Replies: 4

Let a,b be real numbers, and let x_1, x_2 be the roots of the quadratic equation x^2+ax+b=0.

Prove that if x_1, x_2 are real and nonzero,

, and b>0, then |a+2|>2.Thanks. Sorry I forgot to place the [math] tags...

**thedarktiger**- Replies: 4

Prove that if w,z are complex numbers such that |w|=|z|=1 and wz\ne -1, then \frac{w+z}{1+wz} is a real number.

(p+q+r)^2 = 7^2

and

p^2+q^2+r^2 = 9

and set

(p+q+r)^2-40 = p^2+q^2+r^2

then

(p^2+2 p q+2 p r+q^2+2 q r+r^2)-p^2-q^2-r^2 = 40

and 2 p q+2 p r+2 q r = 40

p q+p r+q r = 20,

but it askes for the average so the answer is 10, right?

well it says that is incorrect

Thank you guys so much!

These problems were completely beyond me...

**thedarktiger**- Replies: 10

1) Compute the sum

2) Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations:

3) Suppose p+q+r = 7 and p^2+q^2+r^2 = 9. Then, what is the average (arithmetic mean) of the three products pq, qr, and rp?

4) Find the largest four-digit value of t such that

is an integer.