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

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(13200) (Show Source): You can put this solution on YOUR website!

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

a=9
b=3k
c=k

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(52780) (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.

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