anonymous
  • anonymous
State how many imaginary and real zeros the function has. f(x) = x^3 - 20x^2 + 123x - 216
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ganeshie8
  • ganeshie8
familiar wid Descartes rule of signs ?
anonymous
  • anonymous
I am familiar with it but need to be reminded
ganeshie8
  • ganeshie8
ok take f(x) how many sign changes do u see ?

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anonymous
  • anonymous
2?
ganeshie8
  • ganeshie8
try again
ganeshie8
  • ganeshie8
u need to see how many times the sign is changing
ganeshie8
  • ganeshie8
f(x) = x^3 - 20x^2 + 123x - 216 ^ ^ ^
anonymous
  • anonymous
Okay 3
ganeshie8
  • ganeshie8
good :), now find f(-x), and count sign changes
ganeshie8
  • ganeshie8
f(x) = x^3 - 20x^2 + 123x - 216 f(-x) = ?
anonymous
  • anonymous
So do the inverse? I'm stupid forgive me.
ganeshie8
  • ganeshie8
hey first tim eyou doing this, i can understand...
ganeshie8
  • ganeshie8
to find f(-x), just replace all x with -x
ganeshie8
  • ganeshie8
f(x) = x^3 - 20x^2 + 123x - 216 f(-x) = (-x)^2 - 20(-x)^2 + 123(-x) - 216
anonymous
  • anonymous
x-20x-123-216 or am I completely off
ganeshie8
  • ganeshie8
you're right ! but i was wrong
ganeshie8
  • ganeshie8
f(x) = x^3 - 20x^2 + 123x - 216 f(-x) = (-x)^3 - 20(-x)^2 + 123(-x) - 216
ganeshie8
  • ganeshie8
i did a typo, its (-x)^3, its not (-x)^2
ganeshie8
  • ganeshie8
f(x) = x^3 - 20x^2 + 123x - 216 f(-x) = (-x)^3 - 20(-x)^2 + 123(-x) - 216 = -x^3 - 20x^2 - 123x - 216
ganeshie8
  • ganeshie8
now tell me, how many sign changes u see in f(-x) ?
anonymous
  • anonymous
None?
ganeshie8
  • ganeshie8
Yes, so we conclude like this :- 3 sign changes in f(x), so number of positive zeroes = 3, or 1 0 sign changes in f(x), so number of negative zeroes = 0 so total number of real zeroes = 3 or 1
ganeshie8
  • ganeshie8
that gives number of imaginary zeroes = 0 or 2
ganeshie8
  • ganeshie8
see if that makes some sense
anonymous
  • anonymous
0 imaginary and 3 real?
ganeshie8
  • ganeshie8
0 imaginary and 3 real or 2 imaginary and 1 real
ganeshie8
  • ganeshie8
Both are true.
ganeshie8
  • ganeshie8
Both are true according to Descarted rule of signs. But when we solve it we will see that "0 imaginary and 3 real" is the correct one.
anonymous
  • anonymous
Thank you so much, you are a champion.
ganeshie8
  • ganeshie8
omg thank you :) im not champion, you're the champion cuz you learning things very fast :)

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