If one of the roots of the equation x²-x+1=0 is α then prove that the other root is -α².Moreover prove that (i) The sum of the roots = 1 (ii) the product of the roots = 1.
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this quadratic have no real roots but the imaginary roots can say complex roots
the root of this equation is -omega and -(omega )^2
thus it is in the form of -alpha and -(alpha)^2
where omega is the cube root of unity
omega = -1+√3i/2
and i = √-1
and sum of roots = -b/a
on comparing eqn with general eqn a= 1
b= -1
c= 1
thus sum = 1
and product of roots = c/a = 1
the root of this equation is -omega and -(omega )^2
thus it is in the form of -alpha and -(alpha)^2
where omega is the cube root of unity
omega = -1+√3i/2
and i = √-1
and sum of roots = -b/a
on comparing eqn with general eqn a= 1
b= -1
c= 1
thus sum = 1
and product of roots = c/a = 1
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