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1. ### Find all integer values k for which p(x)=x³-(k+1)x+2k=0 has a rational root.?

Hello, x³ – (k + 1)x + 2k = 0 = = = = = = = = = = = = = = = = = = = = = = Obviously, if k=0, we obtain... prime and k≠0: Then 2k has four divisors: 1, 2, k and 2k. Rational root theorem induce that if a rational root exists...

2 Answers · Science & Mathematics · 10/12/2012

2. ### What would you subtract from each side to solve for k?

Goal: To get "k" isolated by itself. a.) 0 = 14 + k In order to isolate... so that the 3.3 on the variable side will turn into 0 and will not count. -0.8 = k + 3.3 -0.8 - 3.3 = k + 3.3 - 3.3 -4.1 = k + 0 Since the zero does...

3 Answers · Science & Mathematics · 16/06/2011

3. ### an=sum k=0 to k=n from 10 (-k^2).The limit of this sequence belongs to the set a)Q b) [-1,0) c) R/Q?

a(n) = Σ(k = 0 to ∞) 10^(-k^2) is irrational (choice C, assuming you mean...bit more, showing that it is transcendental. Let p(n) = Σ(k = 0 to n) 10^(n - k^2) and q(n) = 10^n. Then, |Σ(k = 0 to ∞) 10...

2 Answers · Science & Mathematics · 13/04/2013

4. ### (k - 2) x^2 + (k - 5) x - 5 = 0?

(k - 2)x^2 + (k - 5)x - 5 = 0 The roots are equal if the discriminant... discriminant, b^2 - 4ac, evaluated as follows: (k - 5)^2 - 4(k - 2)(-5) And we want this to be equal to zero. (k...

3 Answers · Science & Mathematics · 06/12/2008

5. ### Show that p_k = p_(k-1) + (3k-2) for k >=2. Conclude that p_n = sum from k=1 to n of (3k-2).?

Let k ≥ 2. Then p_(k - 1) + 3k - 2 = (k - 1)[3(k - 1) - 1]/2 + (6k - 4)/2 = [(k - 1)(3k - 3 - 1) + 6k - 4]/2 = [(k - 1)(3k - 4) + 6k - 4]/2 = (3k² - 7k...

1 Answers · Science & Mathematics · 13/09/2009

6. ### How do you solve k * 3^k = 1,000,000,000 algebraically/on paper?

k * 3^k = 1,000,000,000 Start by taking the natural logarithm of both sides of the equation to remove that variable from the exponent:*** ln(3^k)(k) = ln(1,000,000,000) Now the exponent of a factor here can be ...

1 Answers · Science & Mathematics · 21/09/2008

7. ### Solving Polynomial Equations k(k-5)>0?

k(k - 5) > 0 in two cases: 1) k > 0 and (k - 5) > 0 2) k < 0 and (k - 5) < 0 In case 1, k > 0 and k > 5; both of these are true when k > 5. In case 2, k...

1 Answers · Science & Mathematics · 11/04/2010

8. ### Find k such that the equation kx^2+x+64k=0?

k=(-x)/(x^2+64)

1 Answers · Science & Mathematics · 09/10/2007

9. ### Solve -7k + 5 + k = 47 k =?

-7k + 5 + k = 47 -6k=47-5 k=42/(-6) k=-7

2 Answers · Science & Mathematics · 06/11/2011

10. ### Simplify the following factorial:(2k+1)!/(2)(k!)?

(2k+1) * (2k) * (2k-1) * ... * (k+2) * (k+1) / 2 = (2k+1) * k * [(2k-1) * ... * (k+2) * (k+1)] In...ellipsis notation from becoming ambiguous. (Otherwise the k factor is out of sequence and makes that notation unclear.)

1 Answers · Science & Mathematics · 18/07/2011