## cwtan Find the range of $$\Huge \frac {3x^2-2x-1}{x^2+x+2}$$ if x is real. one year ago one year ago

1. Jemurray3

Is calculus available as a tool for this?

2. cwtan

I dun think it need calculus.....

3. Jemurray3

No, but it would be quite straightforward if you used it.

4. cwtan

but this is a 4 mark question and i need the steps to get the mark...... if use calculus i dun think i can get full mark for this question.... (at least 1 mark 1 step)

5. Jemurray3

okay, well that sounds like there's a particular way you're supposed to do it. What class is it?

6. cwtan

Polynomial/

7. Jemurray3

I'm not sure what you mean by that. Is it an algebra class or something? And does it ask you to complete a series of 4 steps?

8. cwtan

somtething like: http://www.stpmwiki.com/index.php/Polynomials_Part2

9. cwtan
10. Jemurray3

whoa whoa whoa. Are you looking for a range or a remainder?

11. cwtan

i duno which part can be use to find the range :( but i know the syllabus is just in that 2 webpage

12. Jemurray3

I say again, just to clarify... you're looking for the range of the function? Which means all of the possible values it could take? Or you're looking for the remainder of the fraction once you've divided?

13. cwtan

find the range for the fraction possible

14. ganeshie8

lets say, $$\frac {3x^2-2x-1}{x^2+x+2} = k$$ => $$3x^2-2x-1 = k(x^2+x+2)$$ $$(3-k)x^2 + (-2-k)x + (-1-2k) = 0$$

15. cwtan

Thank you veryyyy much!!

16. ganeshie8

since, x is real, $$b^2 - 4ac >= 0$$ => $$(2+k)^2 - 4(k-3)(1+2k) >= 0$$ $$(k-4)(k+4/7) >= 0$$

17. ganeshie8

np :)

18. Jemurray3

I like that! I've never done it that way before. @cwtan I'm somewhat surprised that this is a viable technique for you in this instance given what I read in your syllabus, but I suppose if it works it works.

19. ganeshie8

yea this is fallback option when calculus is not allowed.... mukushla taught me this few few days back... :)