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Which pairs are solutions to the equation?
That depends on the equation.
How can you determine whether a polynomial equation has imaginary solutions?
To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.
How are the graph of an equation and the set of all solutions of an equation related?
The coordinates of every point on the graph, and no other points, are solutions of the equation.
The solutions of an equation are often called what?
The roots of the equation
How do you know when an equation has an infinite amount of solutions?
If the equation is an identity.
