How many real solutions does the following quadratic equation have?

Question

4x2+x+3=0

(1 point)
Responses

three real solutions
three real solutions

no real solutions
no real solutions

two real solutions
two real solutions

one real solution

Answer 1

To determine the number of real solutions for the quadratic equation $4x^2+x+3=0$, we can use the discriminant method. The discriminant $D$ is calculated using the formula:

$$D=b^2-4ac$$

For the quadratic equation $a{x}^2+bx+c=0$, the coefficients are:

• $a=4$
• $b=1$
• $c=3$

Now, we can compute the discriminant:

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

Since the discriminant $D$ is less than zero ($D<0$), the quadratic equation has no real solutions.

Therefore, the answer is:

no real solutions