How many real number solutions does the equation have?
-8x^2-8-2=0
o solutions
1
2
infinitely many
I get -1/2 so would it be 2?
I figured the discriminant at 244 so infinite?
review the discriminant. If it is positive, there are two real roots.
In this case, b^2-4ac = 0, so there is but one root.
-8x^2-8x-2 = -2(2x+1)^2
How ever did you come up with a discriminant of 244?
244 was on the wrong problem - this one was 0
sorry
To determine the number of real number solutions of the given equation (-8x^2 - 8x - 2 = 0), we can use the quadratic formula:
The quadratic formula states that if we have an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation, a = -8, b = -8, and c = -2. Plugging these values into the formula, we get:
x = (-(-8) ± √((-8)^2 - 4(-8)(-2))) / (2(-8))
Simplifying:
x = (8 ± √(64 - 64)) / (-16)
x = (8 ± √0) / (-16)
x = (8 ± 0) / (-16)
x = 8/(-16) = -1/2
As you correctly calculated, the value of x is -1/2.
Since the discriminant (b^2 - 4ac) is equal to 0, meaning the square root part of the quadratic formula is 0, we only have one real number solution, which is -1/2.
Therefore, the correct answer is 1 solution.