Question

A quadratic equation with rational coefficients one of whose roots is tan(Pie/12) is

Answer 1

Tan (pi/12) = 2- rt3
Since irrational roots always occur in conjugate pairs
Therefore other root = 2+ rt3
a= 2-rt3 b= 2+ rt3
Therefore the quadratic equation
x^2 - (a+b) x + ab
x^2 -( 2- rt3 + 2 + rt3) x + (2-rt3)(2+rt3)
x^2- 4x + 1= 0 is the required quadratic equation