## NotTim 3 years ago Solve the following equation, xe[2,0pi]. tan^3x-9tan^2x+17tanx-6=0

1. NotTim

Well I tried putting x=1, I got an error.

2. ricnus

$x \approx3.14159 n+1.10715$ $x \approx3.14159 n+0.429998$ $x \approx3.14159 n+1.4191$

3. myininaya

first see if you can solve this $u^3-9u^2+17u-6=0$

4. JamesJ

Thanks myin; that's the way.

5. myininaya

if you try u=2, you will see you have one solution

6. LagrangeSon678

thats what i wasn gonna say replace tan with a variable

7. myininaya

then using synthetic division you can find the other 2 solutions

8. NotTim

I dunno what that is.

9. myininaya

synethic division+quadratic formula (or perhaps factoring if we have other rational zeros)

10. nubeer

u can also urs long division to get factors

11. NotTim

Wait a sec guys, I'm trying to understand this all...

12. JamesJ

A fancy way of saying that as u = 2 is a solution, (u-2) must be a factor of the polynomial. Hence you can write $u^3−9u^2+17^u−6 = (u-2)q(u)$ for some second order polynomial

13. JamesJ

make that 17u, not 17^u

14. myininaya

lol

15. NotTim

What happened to tan?

16. JamesJ

i'll let the other chefs take over

17. myininaya

we will get back to the tan business after we solve that polynomial=0 for u

18. NotTim

Ok, so I'm doing the whole F(#) thing at this point right?

19. myininaya

what?

20. myininaya

what does F(#) mean?

21. NotTim

Looking for the value of x that makes everything 0.

22. ricnus

u = 2 u = 1/2 (7-sqrt(37)) u = 1/2 (7+sqrt(37))

23. FoolForMath

If you think how myininaya magically found that $$u=2$$ there is a analytical way of doing it which is known as Rational root test.

24. myininaya

right fool

25. NotTim

What if I got an error on my calculator?

26. NotTim

Useless its tanx (as an entirety) that I using....

27. LagrangeSon678

Your trying to plug number right into the equation?

28. myininaya

i went through the possible rational zeros and found a rational zero i didn't go through all possible rational zeros as i only needed one so i can just mess with a quadratic

29. NotTim

Lagrange, yes...

30. NotTim

Not the right idea huh?

31. FoolForMath

You need to NotThink a bit.

32. NotTim

...ok? I do that a lot.

33. LagrangeSon678

Follow those steps that myin showed, youll end with the right answers

34. NotTim

I'm just looking at this and my notes, and I have not a clue.

35. NotTim

Is u=tanx?

36. myininaya

yes

37. NotTim

Ok.

38. FoolForMath

it's more like Let u = tan x then form a polynomial in u, factor it and then substitute back the u =tan x and then solve it ..

39. NotTim

ERkk.

40. NotTim

Imma do this slowly... If yo ugotta do something while you help me, do it now as I work this thru...

41. NotTim

IS factor Thereom involved?

42. PaxPolaris

yes...if u-2 is a factor of P(u) ...P(2)=0

43. PaxPolaris

Let tan (x) = u $u ^{3}-9u ^{2}+17u-6=0$ $\left( u-2 \right)\left( u^2 - 7u -3\right) =0$

44. NotTim

wait wait waitt.... And that's also not how I was taught (or shown in the notes). I'll try it out after I'm done my thing tho/.

45. NotTim

Sorry about that. My internet went wonky.

46. NotTim

And now I divide the thing by u-2 right?

47. myininaya

u^2-7u+3 ____________________ u-2| u^3-9u^2+17u-6 -(u^3-2u^2) ------------------- -7u^2+17u-6 -(-7u^2+14u) --------------- 3u-6 -(3u-6) -------- 0

48. NotTim

ok

49. myininaya

pax did i make a mistake?

50. myininaya

our factorizations are a lttle different i have $\left( u-2 \right)\left( u^2 - 7u +3\right) =0$

51. FoolForMath

myininaya, I wish If I can give you more medals for your patience.

52. NotTim

Lol.

53. myininaya

are you talking about me and my division above? lol

54. NotTim

I think just waiting for me to finish up my stuff here. Thanks by the way.

55. myininaya

oh i had a thing i was doing lol

56. PaxPolaris

sorry u r right. it's +3

57. NotTim

ITs +3?

58. myininaya

just making sure when it gets late i tend to screw up on little things

59. myininaya

like sometimes i don't know how to add or multiply sometimes

60. myininaya

we were talking about this: $\left( u-2 \right)\left( u^2 - 7u +3\right) =0$

61. NotTim

ok. that scared me for a sec.

62. FoolForMath

yep myininaya I was talking about that :D

63. myininaya

lol

64. myininaya

so we know we have u=2 we also have $u=\frac{7 \pm \sqrt{49-4(3)}}{2}$ don't forget to replace u with tan(x) and solve for x

65. NotTim

Finally, I'm done the division.

66. myininaya

lol

67. myininaya

good

68. myininaya

you have $u-2=0 \text{ or } u^2-7u+3=0$

69. myininaya

we need to use the quadratic formula to solve the second equation

70. NotTim

I hope I remember this for the test.

71. myininaya

so this is trig class?

72. myininaya

i could be wrong but this is too long to put on a test

73. myininaya

there might be a similar problem he/she puts there

74. myininaya

but shorter

75. NotTim

Whoops. I didn't type that...Double post or something.

76. myininaya

i could be wrong

77. LagrangeSon678

sometimes teachers get problems from special books

78. myininaya

I'm sleepy guys I'm sure if you need more help NotTim (who we decided was not myininaya earlier ;)lol) , fool and pax will continue to help unless they are are going.

79. NotTim

K. Thanks man.

80. myininaya

Do I look like a man to you?

81. myininaya

82. myininaya

lol

83. NotTim

Are you?

84. NotTim

I actually have bad vision and human identification problems.

85. NotTim

When I'm walking around I will misidentify everyone as the same person.

86. myininaya

Ok. Its cool. No worries.

87. NotTim

any1 know what I should do at (m-2)(m^2-7m+3)?

88. NotTim

For m^2-7m+3, do I have to do the quadratic formula?

89. NotTim

I guess I already know what to do with m-2, so I'm fine there.

90. NotTim

ERm, are you people just gunna lurk there? It's fine, just....

91. ktklown

find all places that u can be 0, then, recalling that u = tanx, solve for x.

92. ktklown

you already found one solution is u=2, you can find the others by using the quadratic formula on the quadratic part of your factoring.

93. NotTim

Ok.

94. NotTim

Hey, if one of my answers is 6.54, and I wanna get the other angle with it, what do i Do?

95. NotTim

Hi?

96. NotTim

Um, sorry if I sound abrupt, but could anyone please answer my most recent question?