If α , β ∈ R are such that 1 - 2 i (here i 2 = - 1 ) is a root of z 2 + α z + β =…

If α,β∈R are such that 1-2i (here i2=-1) is a root of z2+αz+β=0, then α-β is equal to:
  1. -7
  2. 7
  3. -3
  4. 3

Solution

∵α,β∈R⇒ other root is 1+2i

α=-( sum of roots )=-1-2i+1+2i=-2

β=product of roots =1-2i1+2i=5

∴α-β=-7

option 1

Asked in: JEE Main 2021 (25 Feb Shift 2)

Practice more Quadratic Equation questions on Aicharya