Two cases in which this can typically happen (there are others as well) are:
1. The equation includes a square. Example: x2 = 25; the solutions are 5 and -5.
2. The equation includes an absolute value. Example: |x| = 10; the solutions are 10 and -10.
There are two distinct real solutions.
A quadratic equation can have two solutions, one solution, or no real solutions, depending on its discriminant (the part of the quadratic formula under the square root). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is exactly one real solution (a repeated root); and if it is negative, there are no real solutions, only complex ones. Thus, a quadratic equation does not always have two solutions.
They each typically have two solutions, a positive one and a negative one.
A linear equation in two variables represents a straight line on a Cartesian plane. Each point on this line corresponds to a unique pair of values for the two variables that satisfy the equation. Since there are infinitely many points on a line, there are also infinitely many solutions to the equation. Thus, any linear equation in two variables has an infinite number of solutions.
Normally it has two solutions but sometimes the solutions can be the same.
The quadratic equation will have two solutions.
There are two distinct real solutions.
If the highest degree of an equation is 3, then the equation must have 3 solutions. Solutions can be: 1) 3 real solutions 2) one real and two imaginary solutions.
A quadratic equation can have two solutions, one solution, or no real solutions, depending on its discriminant (the part of the quadratic formula under the square root). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is exactly one real solution (a repeated root); and if it is negative, there are no real solutions, only complex ones. Thus, a quadratic equation does not always have two solutions.
They each typically have two solutions, a positive one and a negative one.
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
The number of solutions an equation has depends on the nature of the equation. A linear equation typically has one solution, a quadratic equation can have two solutions, and a cubic equation can have three solutions. However, equations can also have no solution or an infinite number of solutions depending on the specific values and relationships within the equation. It is important to analyze the equation and its characteristics to determine the number of solutions accurately.
No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2
An absolute value equation typically has two solutions if it can be expressed in the form (|x| = a) where (a) is a positive number. This means the equation has two scenarios: (x = a) and (x = -a). If the equation is set equal to a negative number, it has no solution, and if it's equal to zero, there is only one solution. Therefore, check the right side of the equation to determine the number of solutions.
The equation has two real solutions.
A linear equation in two variables represents a straight line on a Cartesian plane. Each point on this line corresponds to a unique pair of values for the two variables that satisfy the equation. Since there are infinitely many points on a line, there are also infinitely many solutions to the equation. Thus, any linear equation in two variables has an infinite number of solutions.
Two distinct real solutions.