Question

What is the number of real solutions?
-11x^(2)=x+11
A. cannot be determined
B. one solution
C. two solutions
D. no real solutions

Answer 1

To determine the number of real solutions to the equation, we can start by rearranging the equation to set it equal to zero:

-11x^2 - x - 11 = 0

To solve this quadratic equation, we can apply the quadratic formula:

x = [-b ± √(b^2 - 4ac)] / (2a)

In this equation, a = -11, b = -1, and c = -11.

Plugging in the values, we get:

x = [1 ± √((-1)^2 - 4(-11)(-11))] / (2(-11))
x = [1 ± √(1 - 484)] / (-22)
x = [1 ± √(-483)] / (-22)

Since we have the square root of a negative number in the equation, we can conclude that there are no real solutions to the equation.

Therefore, the answer is D. no real solutions.