Question

Which of the following is a solution of x2 + 4x + 10?

2 + i times the square root of 6
−2 + i times the square root of 24
−2 + i times the square root of 6
2 + i times the square root of 24

Answer 1

x^2+4x+10=0

x^2+4x=-10

x^2+4x+4=-6

(x+2)^2=-6

x+2=±i√6

x=-2±i√6

So the correct answer is the third one down from the top.

Answer 2

`x=2+-i √(6)`

Explanation:

`x^2 + 4x + 10`

To find out the solution we set the expression =0 and solve for x

`x^2 + 4x + 10=0`

Apply quadratic formula to solve for x

`x=(-b+-√(b^2-4ac))/(2a)`

a=1, b=4, c=10 plug in the values in the formula

`x=(-4+-√(4^2-4(1)(10)))/(2a)`

`x=(-4+-√(-24))/(2(1))`

The value of square root (-1) is 'i'

`x=(-4+-2i√(6))/(2)`

Divide each term by 2

`x=2+-i√(6)`