If \[\alpha\], \[\beta\] \[\in\] R are such that 1 - 2i (here i2 = -1) is a root of z2 + \[\alpha\]z + \[\beta\] = 0, then (\[\alpha\] - \[\beta\]) is equal to :
Solutions · 1
Official solution
1 - 2i is the root of the equation. So other root is 1 + 2i
\[ \therefore \] Sum of roots = 1 - 2i + 1 + 2i = 2 = -\[\alpha \]
Product of roots = (1 - 2i)(1 + 2i) = 1 - 4i2 = 5 = \[\beta \]
\[ \therefore \] \[\alpha \] - \[\beta \] = -2 - 5 = -7