Question

How many real solutions does the following quadratic equation have? 4x ^ 2 + x + 3 = 0 point ) real solutions real solution real solutions Othree 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 method. The discriminant \( D \) of a quadratic equation of the form \( ax^2 + bx + c = 0 \) is given by:

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

For the given equation, we have:
- \( a = 4 \)
- \( b = 1 \)
- \( c = 3 \)

Now, we can substitute these values into the discriminant formula:

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

The discriminant \( D \) is negative (\( D < 0 \)), which indicates that the quadratic equation has no real solutions. Therefore, the answer is:

**No real solutions**.