Question

The roots of the quadratic equation _______ are x = 2 ± i.

x^2-4x-5=0
x^2+4x+5=0
x^2-4x+5=0
x^2+4x-5=0

Answer 1

If we solve the 3rd equation x^2-4x+5=0 its roots are
(2 + 1) and (2 - i)

Answer 2

Option 3 is correct that
`x^2-4x+5`

Step-by-step explanation:

To form a quadratic equation from its zeroes we have a formula which is

`x^2-(sum of zeroes)x+product of zeroes`

Here we have been give the two zeroes
`x=2+i` and
`x=2-i`

substituting the values
`x=2+i` and
`x=2-i` in the formula we will get

`x^2-{(2+i)+(2-i)}x+(2+i)(2-i)`

After simplifying the equation we will get
`x^2-4x+5`

Since,
`i^2=-1`

Therefore required equation is :
`x^2-4x+5`