# Which of the following is a solution of x^{2} + 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 x^{2 }+ 4x + 10 is a quadratic equation the general form of which is a2 + bx + c.

The roots of the equation a^{2} + bx + c are:

(-b ± √b^{2} - 4ac)/2a

For the equation x^{2} + 4x + 10

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

Hence the value of

b^{2} - 4a = (4)2 - 4 × 1 × 10 = 16 - 40 = - 24

Therefore

√b^{2} - 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 x^{2} + 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.

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