To determine the number of real solutions for the quadratic equation \(4x^2 + x + 3 = 0\), we can use the discriminant \(D\), which is given by the formula:
\[ D = b^2 - 4ac \]
For the quadratic equation \(ax^2 + bx + c = 0\), we have:
- \(a = 4\)
- \(b = 1\)
- \(c = 3\)
Now, we calculate the discriminant:
\[ D = (1)^2 - 4(4)(3) \] \[ D = 1 - 48 \] \[ D = -47 \]
Since the discriminant \(D\) is negative (\(-47 < 0\)), this indicates that the quadratic equation has no real solutions.
Thus, the correct answer is:
no real solutions.
1 answer