roots of equation -3 and -7 then unit equation
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Under what conditions on complex constants α and β, will the quadratic equation z2+αz+β=0 have (a) real roots, (b) one of the roots on the unit circle |z|=1?
Suppose the quadratic equation has real roots, say z=x. Then,
x2+αx+β=0andx2+α¯x+β¯=0
Eliminating x, ...
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EXCLIMINATING x,
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