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 2 years 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
 2 years 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

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sara1234
 2 years ago
Best ResponseYou've already chosen the best response.1I don't understand what it's asking for is it asking to find positive negitive and complex?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3@sara1234 It's asking for no. of positive or negative zeros.!!

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3Yeah, Using Descartes' Rule of Signs we can determine that. I'll explain you

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3We 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?

sara1234
 2 years ago
Best ResponseYou've already chosen the best response.1isnt there 5 sign changes?

sara1234
 2 years ago
Best ResponseYou've already chosen the best response.1oh never miind i got it

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3So 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?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3Now can you write f(x), it's used to find no. of negative zeros

sara1234
 2 years ago
Best ResponseYou've already chosen the best response.13(x)^58(x)^4+25^38(x)^2+(x)19

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3Good , 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?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3Now count the no. of sign changes here

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3Yeah 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?

sara1234
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah thankssss!! Now we find complex?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3We 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

sara1234
 2 years ago
Best ResponseYou've already chosen the best response.1why do we have to add the ) positive?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3Because 0 could be due to 4 complex roots

sara1234
 2 years ago
Best ResponseYou've already chosen the best response.1theres 4 or 2 positive real zeros but why do we have to add the 0

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3There could be a double quadratic, with 4 roots complex. therefore we won't have any positive zero

sara1234
 2 years ago
Best ResponseYou've already chosen the best response.1thanks for all your help @ash2326 you really helped me :)

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.3you're welcome. did you understand all the things?
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