18jonea
  • 18jonea
For 3x9 –7x6 + 4x3 + 15 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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tkhunny
  • tkhunny
Start counting. You signs are +-++ How many changes do you see?
18jonea
  • 18jonea
4
tkhunny
  • tkhunny
No, you see four signs. It starts positive and changes to negative. That's one sign change. How many more CHANGES are there?

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18jonea
  • 18jonea
2
tkhunny
  • tkhunny
Since you are in the habit of answering with one character, I have to clarify, how many sign changes do you see in +-++? Please answer in a sentence.
18jonea
  • 18jonea
i see 2 sign changes
tkhunny
  • tkhunny
This tells us what about the possible number of positive, real roots?
18jonea
  • 18jonea
well i know there are a possible of 9 complex roots and im not sure about real roots @tkhunny
18jonea
  • 18jonea
is there 2 @tkhunny
tkhunny
  • tkhunny
No, there ARE 9 Complex Roots, counting multiplicities and Real Numbers With 2 sign changes in f(x), we now know that there CAN BE 2 positive Real roots. If it is not 2, it must be different by a multiple of 2. So, 2 or 0 Positive Real Roots. Okay, now state f(-x). What does that thing look like?
18jonea
  • 18jonea
@iGreen
tkhunny
  • tkhunny
So, you're not going to produce f(-x)?

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