Answer:
To determine the number and type of solutions for the quadratic equation 5x² + 40x + 80 = 0, you can use the discriminant (the value inside the square root of the quadratic formula). The discriminant is given by:
Discriminant (D) = b² - 4ac
In this equation, a = 5, b = 40, and c = 80. Substituting these values into the discriminant formula:
D = (40)² - 4 * 5 * 80
D = 1600 - 1600
D = 0
Now, let's interpret the discriminant value (D):
If D > 0, the equation has two distinct real solutions.
If D = 0, the equation has one real solution (a repeated or double root).
If D < 0, the equation has no real solutions (complex solutions).
In this case, D = 0, which means the equation has one real solution. This is because the discriminant is neither positive nor negative; it's exactly zero.
So, the equation 5x² + 40x + 80 = 0 has one real solution, which is a repeated or double root. You can find this solution by solving the equation for x.