Best Answer

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.

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Q: Why are there usually two solutions to a quadratic equation?

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If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.

If the discriminant of the quadratic equation is greater than zero then it will have two different solutions. If the discriminant is equal to zero then it will have two equal solutions. If the discriminant is less than zero then it will have no real solutions.

They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation

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.

Quadratic curves only have two solutions when the discrimant is greater than or equal to zero.

Related questions

It is a quadratic equation that normally has two solutions

It is a quadratic equation that normally has two solutions

The two solutions are coincident.

A quadratic equation can have either two real solutions or no real solutions.

If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.

The quadratic equation will have two solutions.

If the discriminant of the quadratic equation is greater than zero then it will have two different solutions. If the discriminant is equal to zero then it will have two equal solutions. If the discriminant is less than zero then it will have no real solutions.

One of its terms will be squared and it will have two solutions.

Normally it has two solutions but sometimes the solutions can be the same.

Two distinct real solutions.

It will then have two equal real solutions

They each typically have two solutions, a positive one and a negative one.

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