How many real solutions does the following quadratic equation have? 4x2+x+3=0 (1 point) Responses no real solutions no real solutions one real solution one real solution two real solutions two real solutions three real solutions three real solutions

To determine the number of real solutions for the quadratic equation \(4x^2 + x + 3 = 0\), we can use the discriminant, given by the formula:

\[
D = b^2 - 4ac
\]

For the equation \(ax^2 + bx + c = 0\), we have:
- \(a = 4\)
- \(b = 1\)
- \(c = 3\)

Now we can calculate the discriminant:

\[
D = (1)^2 - 4(4)(3) = 1 - 48 = -47
\]

Since the discriminant \(D\) is less than zero (\(D < 0\)), this indicates that the quadratic equation has **no real solutions**.

Thus, the answer is:

**no real solutions**.