A quadratic equation with rational coefficients one of whose roots is

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

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

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