How do you write a rational equation given only the solutions?



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justaguide's profile pic

Posted on (Answer #1)

An equation can be written given the solutions of the equation in the following way. Assume an equation f(x) = 0 has the roots x1 and x2.

The corresponding equation would be (x - x1)(x - x2) = 0

=> x^2 - (x1 + x2)*x + x1*x2 = 0

For a higher order equation with solutions x1, x2, x3..., the corresponding equation is (x - x1)(x - x2)(x - x3)... = 0. This can be simplified to give an equation in the standard form.

The same is applicable for the creation of an equation of any order.

etotheeyepi's profile pic

Posted on (Answer #2)

I don't know what might be meant by "rational equation." but x1 and x2 might also be the solutions to

|x -a| = b, or

(x - a)^2 + (y - b)^2 = k


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