how many real number solutions does the equation have?
-8x^2-8x-2=0
the answer is 1, but why
please and thank you
Well, I'd say the equation has one real number solution simply because it's too tired to handle any more. You see, it's like having a wild party and inviting all sorts of complex numbers, but no one from the real numbers shows up except for one lonely soul who actually solves the equation. Life can be pretty unpredictable, right? Just like this equation. So, it's just one real number solution, and it's a celebration for that one brave soul! Cheers! 🎉💪
To determine the number of real number solutions for the given equation, we can use the quadratic formula.
The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the equation -8x^2 - 8x - 2 = 0, we have a = -8, b = -8, and c = -2.
Plugging these values into the quadratic formula, we get:
x = (-(-8) ± √((-8)^2 - 4(-8)(-2))) / (2(-8))
Simplifying further:
x = (8 ± √(64 - 64)) / (-16)
x = (8 ± √0) / (-16)
x = (8 ± 0) / (-16)
x = 8 / (-16) or x = -8 / (-16)
Reducing the fractions:
x = -1/2 or x = 1/2
So, the equation has two solutions: x = -1/2 and x = 1/2.
Since the question asks for the number of real number solutions, we observe that both of these solutions are indeed real numbers. Hence, the equation has 2 real number solutions, not 1.
Please note that if the question specifies to consider only distinct solutions, then, in this case, the equation has 1 real number solution since the solutions x = -1/2 and x = 1/2 are equal (1/2 = -1/2).
To determine the number of real number solutions for a quadratic equation, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, -8x^2-8x-2=0, we can identify the coefficients as follows:
a = -8, b = -8, c = -2
Now, let's substitute these values into the quadratic formula:
x = (-(-8) ± √((-8)^2 - 4(-8)(-2))) / (2(-8))
x = (8 ± √(64 - 64)) / (-16)
Simplifying further:
x = (8 ± √0) / (-16)
x = (8 ± 0) / (-16)
x = 8 / -16
x = -1/2
Since we obtain a single value for x that satisfies the equation, which is x = -1/2, this means that the equation has one real number solution.
It is worth noting that when the discriminant (b^2 - 4ac) is equal to zero, the quadratic equation will have exactly one real solution.
The number of solutions tells you how many times the function
touches or crosses the x-axis.
h = Xv = -B/2A = 8/-16 = -1/2.
Plug -1/2 into the given Eq. and get Y = 0.
V(-1/2, 0).
The parabola touches the x-axis at the vertex only.
If the vertex was above the x-axis, we'll have 2 solutions.
divide by -2 ... 4 x^2 + 4 x + 1 = 0
factoring ... (2 x + 1)(2 x + 1) = 0
it's a perfect square