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
Answers
GPT 3.5
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.
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.