find the bi-quadratic equation with rational coefficients whose one of the roots is√2 + √-3
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As it is given one of the roots is √2+√-3 = √2+i√3
the remaining three roots are √2-i√3 , -√2-i√3 , -√2+i√3
therefore the biquadratic equation can be
[x-(√2+i√3)][x-(√2-i√3)][x-(-√2-i√3)][x-(-√2+i√3)]
by expanding it we get the final biquadratic equation which is
x^4 - 2x^2 + 49
the remaining three roots are √2-i√3 , -√2-i√3 , -√2+i√3
therefore the biquadratic equation can be
[x-(√2+i√3)][x-(√2-i√3)][x-(-√2-i√3)][x-(-√2+i√3)]
by expanding it we get the final biquadratic equation which is
x^4 - 2x^2 + 49
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