Final answer:
The equation 2x^2 + 3x + 5 = 0 has no real roots.
Step-by-step explanation:
The given equation is 2x^2 + 3x + 5 = 0, and we want to determine the number of real roots it has. We can use the quadratic formula to find the roots of a quadratic equation in the form ax^2 + bx + c = 0. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In our equation, a = 2, b = 3, and c = 5. Now let's substitute these values into the quadratic formula:
x = (-3 ± √(3^2 - 4*2*5)) / (2*2)
Simplifying further, we get:
x = (-3 ± √(-31)) / 4
The expression under the square root, -31, is negative, which means we can't take the square root of a negative number in the real number system. Therefore, the equation 2x^2 + 3x + 5 = 0 has no real roots (option c).