pesfunk wrote:Hi Guys
I'm a little confused with the signs. Could someone please let me know the 2 values of K in this case ?
K^2 - 7K - 18 > 0
Regards
k² - 7k - 18 = 0.
(k+2)(k-9) = 0.
Roots are k=-2 and k=9. These are the critical points where the graph crosses the x axis.
If you understand the graph of a parabola:
Since the coefficient in front of k² is positive (the coefficient is 1), the graph of y = k² - 7k - 18 is a parabola that opens upward and crosses the x axis at k=-2 and k=9.
Thus, k² - 7k - 18 > 0 -- in other words, the graph will be above the x axis -- when k<-2 or k>9.
If you don't understand the graph of a parabola:
Plug in a value that is less than the smaller critical point (-2), between the two critical points (-2 and 9), and greater than the larger critical point (9).
k< -2:
If k = -3, then k² - 7k - 18 = (-3)² - (7)(-3) - 18 = 9+21-18 = 12.
Since the result is positive, k² - 7k - 18 > 0 when k< -2.
-2<k< 9:
If k=0, then k² - 7k - 18 = 0² - 7*0 - 18 = -18.
Since the result is negative, k² - 7k - 18 < 0 when -2<k< 9.
k>9:
If k=10, then k² - 7k - 18 = (10)² - (7)(10) - 18 = 100 - 70 -18 = 12.
Since the result is positive, k² - 7k - 18 > 0 when k > 9.
Thus, k² - 7k - 18 > 0 when k<-2 or k>9.
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