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

1. vinrar

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

factorise it and find zeros and use tabe

3. sauravshakya

table method not tabe

4. strawberry_militia

@sauravshakya what is the table method?

5. amistre64

table method: sit down at the table with pencil and paper :)

6. sauravshakya

I will do for easy one ok suppose |dw:1344005362435:dw|

7. nickhouraney

can you find the zeros then use synthetic division to reduce it to a smaller factor?

8. sauravshakya

here |dw:1344005426187:dw|

9. amistre64

can you use calculus?

10. strawberry_militia

no

11. amistre64

x^4 + .... has the shape|dw:1344005576425:dw| knowing the min and max parts would be useful

12. sauravshakya

|dw:1344005474076:dw| now using table |dw:1344005508829:dw|

13. sauravshakya

so from the table we get|dw:1344005614786:dw|

14. sauravshakya

got it @strawberry_militia

15. sauravshakya

use this similar method to solve your question @strawberry_militia

16. amistre64

well, a quick trial and error gives me one zero: f(0) = 6 f(1) = 0

17. amistre64

that should reduce it to a cubic

18. strawberry_militia

I have found the factors.

19. amistre64

then plot them on a number line and take test point between the zeros to determine signage

20. vinrar

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

to -inf and +inf should be positive just by the nature of the poly

22. vinrar

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

so when you get a positive value..that is your required range

24. strawberry_militia

I will try it out. thanks for all your responses.