How many real number solutions exist for 2x2 8x 8 = 0?
It would help if you proofread your questions before you posted them. You need to include all the signs for addition and/or subtraction. Also online "^" is used to indicate an exponent, e.g., x^2 = x squared.
Is this your equation?
2x^2 ± 8x ± 8 = 0
Assuming the signs are positive,
(2x+4)(x+2) = 0
x = -2
Well, let's solve this equation together and find out! We can start by using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 2, b = 8, and c = 8. Plugging those values into the formula, we get x = (-8 ± √(8^2 - 4*2*8)) / (2*2). Simplifying further, we have x = (-8 ± √(64 - 64)) / 4. Since the term inside the square root is 0, we end up with x = (-8 ± 0) / 4. And anything divided by 4 is still the same thing! So, we have x = -8/4 = -2. Therefore, the equation has only one real number solution, and that's x = -2.
To find the number of real number solutions of the equation 2x^2 + 8x + 8 = 0, we can use the discriminant formula.
The discriminant (D) of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.
In this case, a = 2, b = 8, and c = 8.
Substituting these values into the discriminant formula, we have:
D = (8)^2 - 4(2)(8)
D = 64 - 64
D = 0
The discriminant is zero.
When the discriminant is equal to zero, the quadratic equation has two equal real solutions.
Therefore, the equation 2x^2 + 8x + 8 = 0 has exactly one real number solution.
To determine the number of real number solutions for the quadratic equation 2x^2 + 8x + 8 = 0, you can use the discriminant formula. The discriminant is given by the expression b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0.
In this case, a = 2, b = 8, and c = 8. Let's calculate the discriminant:
b^2 - 4ac = 8^2 - 4(2)(8) = 64 - 64 = 0
The value of the discriminant is 0.
Now, based on the value of the discriminant, we can determine the number of real number solutions:
1. If the discriminant is positive (greater than 0), then the quadratic equation has two distinct real number solutions.
2. If the discriminant is zero, then the quadratic equation has one real number solution.
3. If the discriminant is negative (less than 0), then the quadratic equation has no real number solutions.
In our case, since the discriminant is 0, the quadratic equation 2x^2 + 8x + 8 = 0 has one real number solution.