How many real solutions does the following quadratic equation have?

Question

4x^2 + x + 3 = 0
A. two real solutions
B. no real solutions
C. three real solutions
D. one real solution

Answer 1

Using the quadratic formula, we can find the discriminant of the quadratic equation. The discriminant is calculated as $b^2 - 4ac$, where $a$, $b$, and $c$ are the coefficients of the quadratic equation. In this case, $a = 4$, $b = 1$, and $c = 3$, so the discriminant is $1^2 - 4(4)(3) = 1 - 48 = -47$. Since the discriminant is negative, the quadratic equation has no real solutions. Therefore, the correct answer is $\boxed{\text{B. no real solutions}}$.