Question

When does a quadratic equation in the form ax2+b=c have two real rational solutions?

Answer 1

Hello from MrBillDoesMath!

Answer:

The roots are real and rational when b^2+4ac > 0

Discussion:

I suspect the quadratic equation you meant was

ax^2 + bx = c     (*)

Note: the equation in the Question contains only "b",  not "bx.

Rewriting (*) as

ax^2 + bx + (-c) = 0

and using the quadratic equation gives

x = ( -b +\- sqrt(b^2-4a(-c) ) /(2a)

  = ( -b +\- sqrt(b^2 +4ac) )/(2a)

So the roots (values of x) are real and rational when b^2+4ac > 0 (in this case sqrt(b^2 +4ac) is a real number)

Thank you,

MrB