The quadratic equation in x is x2 + 2x.cos(A) + K=0. &also given summation and difference of solutions of above equation are -1 & -3 respectively. Hence find K & A?

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Answer 1 · 2018-05-05T13:40:02

#A=60^@#
#K=-2#

#x^2+2xcos(A)+K=0#

Let the solutions of the quadratic equation be #alpha# and #beta#.

#alpha+beta=-1#

#alpha-beta=-3#

We also know that #alpha+beta=-b/a# of the quadratic equation.

#-1=-(2cos(A))/1#

Simplify and solve,

#2cos(A)=1#

#cos(A)=1/2#

#A=60^@#

Substitute #2cos(A)=1# into the equation, and we get an updated quadratic equation,

#x^2+x+K=0#

Using the difference and sum of roots,

#(alpha+beta)-(alpha-beta)=(-1)-(-3)#

#2beta=2#

#beta=1#

When #beta=1#,

#alpha=-2#

When the roots are #1# and #-2#, we can get a quadratic equation as follows,

#(x-1)(x+2)#

#=x^2+x-2#

By comparison,

#K=-2#