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Q: Why quadratic equations have two solutions?

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

2

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.

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.

If they are quadratic equations then if their discriminant is less than zero then they have no solutions

Related questions

two solutions

Two solutions

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

Yes. It can have 0, 1, or 2 solutions.

Yes and sometimes the two solutions are equal

They are the solutions for the reduced quadratic.

2

A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.

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.

No. A quadratic may have two identical real solutions, two different real solutions, ortwo conjugate complex solutions (including pure imaginary).It can't have one real and one complex or imaginary solution.

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.

If they are quadratic equations then if their discriminant is less than zero then they have no solutions

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