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If a ,b ,c are nonzero real numbers and ...

If `a ,b ,c` are nonzero real numbers and `a z^2=b z+c+i=0` has purely imaginary roots, then prove that `a=b^2cdot`

Text Solution

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Let `ialpha` be a root where `alpha in R`
`rArr - aalpha^(2)+ bialpha + c+ i=0`
`rArr c = aalpha^(2), 1 balpha=0`
`rArr alpha^(2) = (c)/(a), alpha = (-1)/(b)`
`rArr (1)/(b^(2))= (c)/(a) rArr a= b^(2)c`
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