How many real solutions does the following quadratic equation have? 4x2+x+3=0 (1 point) Responses two real solutions two real solutions no real solutions no real solutions three real solutions three real solutions one real solution
The number of real solutions to a quadratic equation can be determined by calculating the discriminant, which is given by b^2 - 4ac. If the discriminant is positive, there are two distinct real solutions. If the discriminant is zero, there is one real solution, and if the discriminant is negative, there are no real solutions.
In the given quadratic equation, the coefficients are a = 4, b = 1, and c = 3. We can calculate the discriminant as follows:
Discriminant = b^2 - 4ac = 1^2 - 4(4)(3) = 1 - 48 = -47.
Since the discriminant is negative, the quadratic equation has no real solutions.
Therefore, the correct response is:
no real solutions.
To determine the number of real solutions for a quadratic equation, we can use the discriminant formula, which is given by:
Δ = b^2 - 4ac
In this equation, a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.
For the quadratic equation 4x^2 + x + 3 = 0, a = 4, b = 1, and c = 3.
Calculating the discriminant:
Δ = (1)^2 - 4 * 4 * 3
= 1 - 48
= -47
The discriminant is negative (-47). This means that there are no real solutions because a negative discriminant indicates that the quadratic equation has complex solutions. Hence, the correct answer is "no real solutions."
To determine the number of real solutions for the quadratic equation 4x^2 + x + 3 = 0, we can use the discriminant.
The discriminant (Δ) is found by substituting the coefficients into the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
For the given equation, a = 4, b = 1, and c = 3. Substituting these values into the discriminant formula:
Δ = (1)^2 - 4(4)(3)
Δ = 1 - 48
Δ = -47
The discriminant is -47. Since the discriminant is negative, there are no real solutions for the quadratic equation.
Therefore, the correct response is "no real solutions."