SOLUTION: Find all positie values for K for which each of the following can be factored.
x^2 + x - k
Thank you for your help.
Algebra.Com
Question 27864: Find all positie values for K for which each of the following can be factored.
x^2 + x - k
Thank you for your help.
Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
It can only be factored if the discriminant is positive and a perfect square. The discriminant is defined by:
for
For your problem a=1, b=1 and c=-k
so the descriminant is
So any number that when multiplied by 4 is one less than a square number would work. Such as:
0 --> 1+4*0=1 -->
2 --> 1+4*2=9 -->
6 --> 1+4*6=25 -->
12 --> 1+4*12=49 -->
20 --> 1+4*20=81 -->
30 --> 1+4*30=121 -->
42 --> 1+4*42=169 -->
Starting to see some paterns, no doubt?...
So there's an infinite number of k's that'll work. To find the next value in the pattern, square each odd number, subtract one, and divide by 4.
Answer your question?
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