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strawberry_militia

  • 2 years ago

P(x)=\[x^4-x^3-7x^2+x+6\] Solve P(x)>0

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  1. vinrar
    • 2 years ago
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    simplify the equation into its factors one factor being x-1 and find other factors then write down the domain of the factors, and you'll see the range is positive in certain domain that's the answer

  2. sauravshakya
    • 2 years ago
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    factorise it and find zeros and use tabe

  3. sauravshakya
    • 2 years ago
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    table method not tabe

  4. strawberry_militia
    • 2 years ago
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    @sauravshakya what is the table method?

  5. amistre64
    • 2 years ago
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    table method: sit down at the table with pencil and paper :)

  6. sauravshakya
    • 2 years ago
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    I will do for easy one ok suppose |dw:1344005362435:dw|

  7. nickhouraney
    • 2 years ago
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    can you find the zeros then use synthetic division to reduce it to a smaller factor?

  8. sauravshakya
    • 2 years ago
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    here |dw:1344005426187:dw|

  9. amistre64
    • 2 years ago
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    can you use calculus?

  10. strawberry_militia
    • 2 years ago
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    no

  11. amistre64
    • 2 years ago
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    x^4 + .... has the shape|dw:1344005576425:dw| knowing the min and max parts would be useful

  12. sauravshakya
    • 2 years ago
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    |dw:1344005474076:dw| now using table |dw:1344005508829:dw|

  13. sauravshakya
    • 2 years ago
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    so from the table we get|dw:1344005614786:dw|

  14. sauravshakya
    • 2 years ago
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    got it @strawberry_militia

  15. sauravshakya
    • 2 years ago
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    use this similar method to solve your question @strawberry_militia

  16. amistre64
    • 2 years ago
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    well, a quick trial and error gives me one zero: f(0) = 6 f(1) = 0

  17. amistre64
    • 2 years ago
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    that should reduce it to a cubic

  18. strawberry_militia
    • 2 years ago
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    I have found the factors.

  19. amistre64
    • 2 years ago
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    then plot them on a number line and take test point between the zeros to determine signage

  20. vinrar
    • 2 years ago
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    write down the factors in coordinates form like if the four factors are a,b,c,d and a<b<c<d then write it as (-infinity,a) (a,b) (b,c) and (c,d)

  21. amistre64
    • 2 years ago
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    to -inf and +inf should be positive just by the nature of the poly

  22. vinrar
    • 2 years ago
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    and (d,infinity) then substitute a value in between (-infinity ,a) and check it is positive or not similiarly do for (a,b) (b,c) and (c,d) and (d,infinity)

  23. vinrar
    • 2 years ago
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    so when you get a positive value..that is your required range

  24. strawberry_militia
    • 2 years ago
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    I will try it out. thanks for all your responses.

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