X^2+3x+5 = 0

To solve the quadratic equation x^2 + 3x + 5 = 0, you can use the quadratic formula (-b ± √(b^2 - 4ac))/2a.

Comparing the given equation to the standard form of a quadratic equation ax^2 + bx + c = 0, we have: a = 1 b = 3 c = 5

Now, substitute these values into the quadratic formula: x = (-3 ± √(3^2 - 4(1)(5))) / 2(1)

Simplifying further: x = (-3 ± √(9 - 20)) / 2 x = (-3 ± √(-11)) / 2

Since the discriminant (√(-11)) is negative, the quadratic equation has no real solutions. Therefore, it does not have any real roots.