Question

HOw can i figure out what the number of complex zeros and why is for given--->
x^4-6x^3+7x^2-6x+6

Answer 1

4?

Answer 2

descartes sign change thrm might be helpful

Answer 3

descartes?

Answer 4

x^4 -6x^3 +7x^2 -6x +6
1 / 1 / 1 / 1 / 0

4 sign changes; there are 4,2,or 0 positive roots; the change is the result of 2 possible complex roots each time

Answer 5

replace x by -x and test again (all the odd powers swap a sign)

x^4 +6x^3 +7x^2 +6x +6
0 /

there are no negative roots to worry about

Answer 6

i see that.. :)

Answer 7

so there is at most 0,2 or 4 complex roots to counter the possible postivie roots

Answer 8

thank youuuu:)

Answer 9

yep, i cant really see a way to make a definitive count tho ...

Answer 10

and for the maximum and minimum number of turning points? I can't see that much on the graph i have but would it be 3

Answer 11

^2 turns once ; as a parabola

^3 turns twice ; like an S

^n turns (n-1) times in general

Answer 12

this poly is a ^4 highest; so it turns 3 times

Answer 13

i get it, thank you very much you made it all make good sense:)))))))

Answer 14

yw