what is the number of real solutions -11x2=x+11
it is a second-degree equation, the number of solutions is 2, you have to do more to find out if any of them are real.
11x^2+x+11=0
x=(-1+- sqrt(1-4*11*11)/22
so, the radical is a squart of a large negative number, so there are no real solutions.
Thank you bob, these types of problems confuse me soooo much.
I'm glad you explained it instead of just giving the answer
Well, this equation is quite the joker! Let's solve it and find out the number of real solutions.
Rearranging the equation, we have -11x^2 - x - 11 = 0.
If we apply the quadratic formula, we get x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in a = -11, b = -1, and c = -11, we have x = (1 ± √(1 - 4(-11)(-11))) / (2(-11)).
Now, let's simplify that mess. Inside the square root, we have 1 - 484, which equals -483. Uh-oh, we just stepped into imaginary territory!
Since we're dealing with a negative value inside the square root, it means this equation has no real solutions, my friend. It's just clowning around with imaginary solutions. How peculiar!
To find the number of real solutions for the equation -11x^2 = x + 11, we can use the quadratic formula.
Step 1: Rearrange the equation to bring all terms to one side, making it equal to zero:
-11x^2 - x - 11 = 0
Step 2: Use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For our equation, a = -11, b = -1, and c = -11. Plugging in these values into the quadratic formula, we get:
x = (-(-1) ± sqrt((-1)^2 - 4(-11)(-11)) / (2(-11))
x = (1 ± sqrt(1 - 484)) / (-22)
x = (1 ± sqrt(485)) / (-22)
Step 3: Determine the nature of the solutions by checking the value inside the square root. If it is positive, there are two distinct real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions.
In our case, sqrt(485) is a positive value, so there are two distinct real solutions for the equation -11x^2 = x + 11.
Therefore, the number of real solutions is 2.
To find the number of real solutions for the given equation -11x^2 = x + 11, we need to solve the equation and determine the values of x that satisfy the equation.
Step 1: Rewrite the equation in standard quadratic form, which is ax^2 + bx + c = 0. Move all terms to one side:
-11x^2 - x - 11 = 0
Step 2: To solve the equation, we can use the quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the current equation, a = -11, b = -1, and c = -11. Substituting these values into the quadratic formula:
x = (-(-1) ± √((-1)^2 - 4(-11)(-11))) / (2(-11))
x = (1 ± √(1 - 484)) / (-22)
x = (1 ± √(-483)) / (-22)
Step 3: Simplify the square root expression. Since the radicand (-483) is negative, we know that there are no real solutions to this equation. This is because the square root of a negative number is not a real number.
Therefore, the given equation -11x^2 = x + 11 has no real solutions.