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Q: Why are there usually two solutions in quadratic equations and when do they only have one solution?

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In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.

That's not an equation - it doesn't have an equal sign. Assuming you mean 2x2 - 3x - 90 = 0, you can find the solution, or usually the two solutions, of such equations with the quadratic formula. In this case, replace a = 2, b = -3, c = -90.

The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.

The set of points the graphed equations have in common. This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.

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.

Related questions

In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.

Quadratic equations like this one usually have two solution. Sometimes they have one (so-called "double") solution. If you solve it, you'll know for sure.

That's not an equation - it doesn't have an equal sign. Assuming you mean 2x2 - 3x - 90 = 0, you can find the solution, or usually the two solutions, of such equations with the quadratic formula. In this case, replace a = 2, b = -3, c = -90.

The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.

The set of points the graphed equations have in common. This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.

the maximum number of solutions to a quadratic equation is 2. However, usually there is only 1.

No, linear equations don't have x2. Equation with x and y are usually linear equations. Equations with either x2 or y2 (but never both) are usually quadratic equations.

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.

It is used to solve quadratic equations that cannot be factored. Usually you would factor a quadratic equation, identify the critical values and solve, but when you cannot factor you utilize the quadratic equation.

It is easier to understand this if you draw the curve of the equation as a graph. From the graph you will see that the line curves back on itself, usually in a nice parabolic curve. Because it curves back, you find that most values of Y correspond to two different values of X - so there are two solutions.

By removing the water - usually by heating the solution up.

It depends on the equation. The equations we normally deal with in real life usually have one, however, equations can have a potentially infinite number of answers.

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