Use the discriminant to determine how many real number solutions the equation has.
t^2 + 8t + 16 = 0
discriminant= b2-4ac
(8)^2-4(1)(16)
64-64=0
One real root (because it equals 0).
If it was a positive number, there would be two real roots. If it was a negative number, there would be two COMPLEX roots.
To use the discriminant to determine the number of real number solutions an equation has, we first need to identify the formula for the discriminant. For a quadratic equation in the form ax^2 + bx + c = 0, the discriminant (D) is given by:
D = b^2 - 4ac
Now let's apply this to the equation t^2 + 8t + 16 = 0:
In this case, a = 1, b = 8, and c = 16.
Substituting these values into the discriminant formula, we have:
D = 8^2 - 4(1)(16)
D = 64 - 64
D = 0
The discriminant is zero in this case.
Now, based on the discriminant's value, we can determine the number of real number solutions:
1. If the discriminant is greater than zero (D > 0), the equation has two distinct real number solutions.
2. If the discriminant is equal to zero (D = 0), the equation has one real number solution (a repeated root).
3. If the discriminant is less than zero (D < 0), the equation has no real number solutions (only complex solutions).
In this case, since the discriminant is zero, the equation t^2 + 8t + 16 = 0 has one real number solution (a repeated root).
To determine the number of real number solutions of the quadratic equation t^2 + 8t + 16 = 0, we can use the discriminant.
The discriminant is the expression b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In the given equation, a = 1, b = 8, and c = 16. Substituting these values into the discriminant formula:
Discriminant = (8)^2 - 4(1)(16)
= 64 - 64
= 0
The discriminant is equal to 0.
The value of the discriminant determines the number of real number solutions of a quadratic equation:
- If the discriminant is greater than 0, then the equation has two distinct real solutions.
- If the discriminant is equal to 0, then the equation has one real solution.
- If the discriminant is less than 0, then the equation has no real solutions.
In this case, since the discriminant is equal to 0, the quadratic equation t^2 + 8t + 16 = 0 has one real solution.