SOLUTION: For what values of k will the graph of y = 9x^2+3kx+k have no x-intercepts?

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Question 1180170: For what values of k will the graph of y = 9x^2+3kx+k have no x-intercepts?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


When the discriminant b^2-4ac is negative.

a=9
b=3k
c=k

b%5E2-4ac=%283k%29%5E2-4%289%29%28k%29=9k%5E2-36k

9k%5E2-36k%3C0
k%5E2-4k%3C0
k%28k-4%29%3C0

The graph of k(k-4) is a parabola that opens upward, with zeros at k=0 and k=4. So the value of the expression is negative only between 0 and 4.

ANSWER: 0 < k < 4

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

If and only if the discriminant of the quadratic function is NEGATIVE


    d = b^2 - 4ac = (3k)^2 - 4*9*k < 0


    9k^2 - 36k < 0

     k^2 - 4k < 0

     k*(k-4) < 0

     0 < k < 4.


               A  N  S  W  E  R  


   +-------------------------------------------+
   |     the given graph has no x-intercepts   |
   |             for  0 < k < 4.               |
   +-------------------------------------------+

Solved, answered and explained.