Question

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

Answer 1

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**.