Question

How many real solutions does 4x squared+ x + 3 = 0 1/2

Answer 1

To determine how many real solutions the equation \(4x^2 + x + 3 = 0\) has, we can use the discriminant from the quadratic formula.

For a quadratic equation of the form \(ax^2 + bx + c = 0\), the discriminant \(D\) is given by:

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

For the equation \(4x^2 + x + 3 = 0\):
- \(a = 4\)
- \(b = 1\)
- \(c = 3\)

Now, we calculate the discriminant:

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

Since the discriminant \(D\) is negative (\(-47 < 0\)), this means that the quadratic equation has no real solutions; it has two complex solutions.

So, the answer is that the equation \(4x^2 + x + 3 = 0\) has **0 real solutions**.