Question

Can someone help me please?
tan^2(x) +5 tan(x) +3=0
Approximate to four decimal places the solutions for x,
0 less than or equal to x<2pi

Answer 1

\[\tan ^{2}x+5\tan x+3=0\]
using quadratic equation
\[\frac{ -5\pm \sqrt{5^{2}-4(1)(3)} }{ 2(1) }\]
so
\[\frac{ -5\pm \sqrt{25-12} }{ 2 }\]
\[\frac{ -5\pm \sqrt{13} }{ 2 }\]
\[\frac{ -5+\sqrt{13} }{ 2 }=-.6972 \]
or
\[\frac{ -5-\sqrt{13} }{ 2 }=-4.3028\]
but it is none of my choices?????

Answer 2

Those values are for tan x

Answer 3

So do I need to convert them into sin/cos?

Answer 4

According to those figures there is no solution in the given interval

Answer 5

my choices are
A) 0.8692, 2.2724, 4.0108, 5.4140
B) 0.9041, 2.2375
C) 1.7992, 2.5327, 4.9407, 5.6743
D) 1.2304, 1.9111, 3.1416

Answer 6

http://www.wolframalpha.com/input/?i=tan^2%28x%29+%2B5+tan%28x%29+%2B3%3D0