Of the following, which is the solution to 2x2 + 3x = −5? (6 points) select one: a. the quantity negative three plus or minus i times the square root of thirty one over four b. the quantity negative three plus or minus i times the square root of thirty one over two c. the quantity three plus or minus i times the square root of thirty one over four d. the quantity negative three plus or minus i times the square root of fifty over four

a) The quantity negative three plus or minus i times the square root of thirty one over four.

Step-by-step explanation:

The given equation is

This can be written as

Let's factorize and find the solution.

This is a quadratic equation of the form

Let's compare the given equation with the general form and identify the value of a, b and c.

a = 2, b = 3 and c = 5

Here we use quadratic formula to find the solution of this equation.

The quadratic formula x =

Now plug in the value a =2, b = 3 and c = 5 in the above quadratic formula, we get

x =

x =

We know that √-1 = i

So, we get

x =

So the answer is a) The quantity negative three plus or minus i times the square root of thirty one over four.