Question

Which of the following is a solution of x2 + 2x + 4?

A) −2 + two i times the square root of 3
B) 2 + two i times the square root of 3
C) 1 − i times the square root of 3
D) −1 + i times the square root of 3

Answer 1

option-D

Explanation:

we are given

`x^2+2x+4`

Let's assume it is equal to 0

`x^2+2x+4=0`

We can use quadratic formula

Suppose, we are given quadratic equations as

`ax^2+bx+c=0`

`x=(-b\pm √(b^2-4ac))/(2a)`

we can compare and find a,b and c

a=1 , b=2 , c=4

now, we can plug values

and we get

`x=(-2\pm √(2^2-4\cdot \:1\cdot \:4))/(2\cdot \:1)`

now, we can simplify it

and we get

`x=-1+√(3)i,\:x=-1-√(3)i`

Answer 2

The correct option is D) −1 + i times the square root of 3.

Explanation:

We are given the following expression and we are to find the solutions for this quadratic expression:

`x^2 + 2x + 4`

Since we cannot factorize this so we will use the quadratic formula
`x = (-b+-√(b^2-4ac) )/(2a)` to solve it:

`x`
`=`
`(-(2) + -√((2)^2-4(1)(4)) )/(2 (1) )`

`x`
`=`
`-1 + \sqrt {3i} , -1 - \sqrt {3i}`

Therefore, from the given answer options the correct option is D) −1 + i times the square root of 3.