Question

How many true, real number solutions does the equation have? solution(s)

Answer 1

The information provided does not specify the equation in question. To determine the number of true, real number solutions, the specific equation is needed.

Step-by-step explanation:

The number of real number solutions to an equation depends on its mathematical form and properties. If the equation is linear, it may have one solution, infinitely many solutions, or no solution. Quadratic equations can have two real solutions, one real solution (if the discriminant is zero), or no real solutions (if the discriminant is negative). Higher-degree polynomial equations can have varying numbers of real solutions based on their degree and factors.

Without the specific equation mentioned in the question, it's impossible to determine the number of real solutions accurately. A detailed analysis of the equation, including its degree, coefficients, and mathematical properties, is required to ascertain the solution set. Different types of equations necessitate distinct approaches to determine the number and nature of solutions.

In summary, to determine the number of true, real number solutions for an equation, it's crucial to have the equation explicitly stated. Each type of equation has unique characteristics that influence the number and nature of its solutions. Without this information, a definitive answer cannot be provided, emphasizing the importance of specifying the equation for an accurate analysis.

Answer 2

A distinct real solution is a solution to an equation that occurs once, and differs in value from other solutions. For example, in the equation above there are two distinct real solutions: x = − 13 2 and x = 13 2 . Since they are different, real numbers, the equation has two distinct real solutions.

The value of the discriminant determines how many solutions the quadratic will have. Equation 1: the discriminant was zero, there was only 1 solution. Equation 2: the discriminant was a negative number, there was no solution. Equation 3: the discriminant was a positive number, there were two solutions.