Range of quadratic equation

[Black mantis]

Find the range of the expression x-2/x^2 + x + 3 where x is real.

Sol: f(x)= x-2/ x^2 + x + 3 = y

x^2 y + xy + 3y = x -2

 

[Dr.Peterson]

Presumably you meant (x - 2)/(x^2 + x + 3 ); the parentheses are essential.

You've made a good start. Now you want to find values of y for which your equation has at least one solution for x, thinking of y as a constant.

Does the discriminant sound useful?

 

[Otis]

Range of quadratic equation …

Hi Black mantis. Here's a quick note about terminology. The given function is not quadratic; it's rational. You're finding the range of a rational function.

PS: If you google keywords like how to find the range of a rational function, you'll see links to many lessons and examples.

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[Black mantis]

Thank you! Information you provided is very helpful. I got confused with the variables to be used as a discriminant