Question

How many real roots would the equation 2x^2 + 3x + 5 = 0 have?

a) Two real roots
b) One real root
c) No real roots
d) It varies depending on the coefficients.

Answer 1

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).