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?

1 Answer
May 5, 2018

A=60^@
K=-2

Explanation:

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