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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.

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Q: When does a equation have two solutions?
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How many solutions will the equation 25 equals 2x squared 6x have?

The quadratic equation will have two solutions.


How many solutions are there if the discriminant of the equation is positive?

There are two distinct real solutions.


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An equation with a degree of three typically has three solutions. However, it is possible for one or more of those solutions to be repeated or complex.


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When you square each side of an equation is the resulting equation equivalent to the original?

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


If the discriminant of an equation is positive.What is true of the equation?

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