Respuesta :
Since it has a negative discriminant, the quadratic equation that does not have a real solution is given by:
−4x2 − 4x − 6 = 0.
What is the discriminant of a quadratic equation and how does it influence the solutions?
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
- If [tex]\mathbf{\Delta > 0}[/tex], it has 2 rational solutions.
- If [tex]\mathbf{\Delta = 0}[/tex], it has 1 rational solutions.
- If [tex]\mathbf{\Delta < 0}[/tex], it has 0 real solutions.
We want [tex]\Delta < 0[/tex], hence, for equation -4x² - 4x - 6, we have that a = -4, b = -4, c = -6, hence:
[tex]\Delta = (-4)^2 - 4(-4)(-6) = 16 - 96 = -80[/tex]
Negative discriminant, hence it does not have a real solution.
More can be learned about the discriminant of a quadratic function at https://brainly.com/question/19776811
#SPJ1
