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July 23rd, 2015, 12:06 PM   #1
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Hi guys.
Here's the question:

Find the coordinates of the stationary points on the graph of y=3x^4-4x^3-12x^2+10, and sketch the graph.
For what values of k does the equation 3x^4-4x^3-12x^2+10=k have
(a) exactly 4 roots (b) exactly 2 roots?

I did the first part and its correct. But I don't understand the second part about the roots.
Thanks for any help!
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July 23rd, 2015, 12:43 PM   #2
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note the graph of the quartic in the attachment ...

k = 7 (in red) intersects the quartic function four times (four roots) ... are there more possible values for k? what range of values would work?

k = -10 (in green) intersects the quartic function twice (two roots) ... are there more possible values for k? are there values of k > 10 that would also intersect the quartic function twice? in total, what range of values would work?
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File Type: jpg quartic.jpg (13.9 KB, 3 views)
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July 23rd, 2015, 11:29 PM   #3
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Thanks so much! I get it now... easy actually!
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