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how you would analyze the zeros of the polynomial function f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 +x – 19 using Descartes’ Rule of Signs
 one year ago
 one year ago
how you would analyze the zeros of the polynomial function f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 +x – 19 using Descartes’ Rule of Signs
 one year ago
 one year ago

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sara1234Best ResponseYou've already chosen the best response.1
I don't understand what it's asking for is it asking to find positive negitive and complex?
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
@sara1234 It's asking for no. of positive or negative zeros.!!
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
Yeah, Using Descartes' Rule of Signs we can determine that. I'll explain you
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
We have the polynomial \[f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 +x – 19\] First step it to count the no. of sign changes in f(x) I'll underline wherever there is a sign change between two consecutive terms i.e from + to  or  to + \[f(x) = –3x^5 \underline{– 8x^4 +25x^3} – 8x^2 +x – 19 \longrightarrow 1st\ change\] \[f(x) = –3x^5 – 8x^4 \underline{+25x^3 – 8x^2} +x – 19 \longrightarrow 2nd\ change\] \[f(x) = –3x^5 – 8x^4 +25x^3 \underline{– 8x^2 +x} – 19 \longrightarrow 3rd\ change\] \[f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 \underline{+x – 19} \longrightarrow 4th\ change\] so there are 4 sign changes, do you get this part?
 one year ago

sara1234Best ResponseYou've already chosen the best response.1
isnt there 5 sign changes?
 one year ago

sara1234Best ResponseYou've already chosen the best response.1
oh never miind i got it
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
So there could be 4 positive zero, However, some of the roots may be generated by the Quadratic Formula, and these pairs of roots may be complex. so we have to down count by 2. Either it has 4 or 2 or 0 positive roots. Do you get this?
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
Now can you write f(x), it's used to find no. of negative zeros
 one year ago

sara1234Best ResponseYou've already chosen the best response.1
3(x)^58(x)^4+25^38(x)^2+(x)19
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
Good , we need to simplify it. I'll write that \[f(x)=3(x)^58(x)^4+25(x)^38(x)^2+(x)19\] \[f(x)=3x^58x^425x^38x^2x19\] do you get this?
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
Now count the no. of sign changes here
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
Yeah so it's having 1 negative zero, we can't down count by 2, it'll become 1. So it has 1 negative zero and 4 or 2 or 0 positive zeros. Do you get this?
 one year ago

sara1234Best ResponseYou've already chosen the best response.1
Yeah thankssss!! Now we find complex?
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
We found that there are either 4 or 2 or 0 positive roots. But these could also be complex, so if we have have 4 positive roots there will be 0 complex if we have 2 positive there will be 2 complex or if we have 0 positive there will be 4 complex
 one year ago

sara1234Best ResponseYou've already chosen the best response.1
why do we have to add the ) positive?
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
Because 0 could be due to 4 complex roots
 one year ago

sara1234Best ResponseYou've already chosen the best response.1
theres 4 or 2 positive real zeros but why do we have to add the 0
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
There could be a double quadratic, with 4 roots complex. therefore we won't have any positive zero
 one year ago

sara1234Best ResponseYou've already chosen the best response.1
thanks for all your help @ash2326 you really helped me :)
 one year ago

ash2326Best ResponseYou've already chosen the best response.3
you're welcome. did you understand all the things?
 one year ago
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