solve the equation for solutions over the interval 0360 tan2

solve the equation for solutions over the interval [0,360]. tan^2 theta+7 tan theta +2=0

Solution

given equation is tan^2 theta+7 tan theta +2=0

now we can\'t factor it and this is of the form ax^2 +bx +c =0

where roots are [ -b + sqrt(b^2 -4ac) ]/2a and [ -b - sqrt(b^2 -4ac) ]/2a

so here a=1 b=7 c=2

roots are [ -7 + sqrt(7^2 -4.1.2) ]/2 and  [ -7 - sqrt(7^2 -4.1.2) ]/2

roots are [ -7 + sqrt(49 -8)]/2 and  [ -7 - sqrt(49 -8)]/2

so tan theta =  [ -7 + sqrt(41)]/2 or tan theta =  [ -7 - sqrt(41)]/2

tan theta = [-7 +6.40]/2 or tan theta = [-7 -6.40]/2

tan theta = (-0.6)/2 or tan theta =[-13.4]/2

tan theta =-0.3 or tan theta =-6.7

theta = 163.3 , 343.3 or 98.5 , 278.5