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# Why are there usually two solutions to a quadratic equation?

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. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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