If `alpha` is a complex constant such that `a z^2+z+ alpha=0` has a ral root, then `alpha+ alpha=1` `alpha+ alpha=0` `alpha+ alpha=-1` the absolute value of the real root is 1

Options

A. `alph +baralpha =1`
B. `alpha+baralpha=0`
C. `alpha+baralpha= -1`
D. the absolute value of the real root is 1

Answer

A, C, D

Explanation

Let z= c be a real root . Then
`alphac^(2) + c + baralpha = 0" "(1)`
Putting `alpha =p+iq`, we have
`(p+ iq)c^(2) + c+q -iq = 0`
` rArr pc^(2) + c+ p = 0`
`rArr c= pm 1 " "(because q ne 0)`
`therefore (1) rArr alpha pm 1 + baralpha = 0`
Also ,`|c| = 1`