What is the number of real solutions?
12x2 – 11x = 11
(1 point)
Responses
two real solutions
two real solutions
one real solution
one real solution
cannot be determined
cannot be determined
no real solutions
The number of real solutions for the equation 12x^2 - 11x = 11 is one real solution.
To determine the number of real solutions for the equation 12x^2 - 11x = 11, we can start by rearranging the equation to the form: 12x^2 - 11x - 11 = 0.
This is a quadratic equation, so we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this equation, a = 12, b = -11, and c = -11.
Substituting these values into the quadratic formula, we get:
x = (-(-11) ± √((-11)^2 - 4(12)(-11)))/(2(12))
Simplifying further:
x = (11 ± √(121 + 528))/(24)
x = (11 ± √649)/24
Since the discriminant (b^2 - 4ac) is positive and not equal to zero, the quadratic equation has two real solutions.
Therefore, the correct answer is: two real solutions.
To determine the number of real solutions for the equation 12x^2 - 11x = 11, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 12, b = -11, and c = -11. Plugging these values into the quadratic formula, we get:
x = (-(-11) ± √((-11)^2 - 4(12)(-11))) / (2(12))
Simplifying further:
x = (11 ± √(121 + 528)) / 24
x = (11 ± √649) / 24
Since the expression under the square root, 649, is not a perfect square, we can conclude that there are two distinct real solutions for the equation 12x^2 - 11x = 11. Therefore, the answer is "two real solutions".