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

Solution:

The equation x² + 4x + 10 is a quadratic equation the general form of which is a2 + bx + c.

The roots of the equation a² + bx + c are:

(-b ± √b² - 4ac)/2a

For the equation x² + 4x + 10

Here a = 1, b = 4, c = 1

Hence the value of

b² - 4a = (4)2 - 4 × 1 × 10 = 16 - 40 = - 24 

Therefore

√b² - 4ac = √-24 = √-4 × 6 = 2 × √6 × √-1 = i2√6 where i = √-1

The solution or roots of the equation are -4/2 ± 2i√6/2

i.e. -2 + i√6 and -2 - i√6

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

Summary:

The solution or roots of the equation are -2 ± i√6 i.e. -2 + i√6 and -2 - i√6,-2 + i times the square root of 6 is the correct option.