Question

Solve the following quadratic equation:

ix² – 4x – 4i = 0

Answer 1

ix² - 4x - 4i = 0

ax² + bx + c = 0

a = i, b = -4, c = -4i

Δ = b² - 4ac

= `(-4)^2 - 4("i")(-4"i")`

= `16 + (4"i")^2`

= 16 + 16i² ..............[i² = -1]

= 16 - 16

Δ = 0

Both roots are equal.

x = `(-"b" ± sqrtΔ)/(2"a")`

= `(-"b")/(2"a")`

= `(-(-4))/(2"i")`

= `4/(2"i")`

x = `2/"i"`

= `(2"i")/"i"^2 = -2"i"` .....∵ [i² = -1]

x = -2i

The roots are -2i, -2i.