Question

How many real solutions does the following quadratic equation have? 4x2+x+3=0 (1 point) Responses two real solutions two real solutions three real solutions three real solutions no real solutions no real solutions one real solution

Answer 1

The number of real solutions of a quadratic equation can be determined by calculating the discriminant. The discriminant (D) of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.

In the given equation, the coefficients are a = 4, b = 1, and c = 3. Calculating the discriminant:

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

Since the discriminant is negative (D < 0), the quadratic equation has no real solutions. Therefore, the correct response is: no real solutions.