How do you determine if a solution to a quadratic equation is rational or irrational by using the discriminant?

1 Answer
Oct 30, 2014

Consider Quadratic Equation ax^2+bx+c=0

the solutions for above quadratic equation are as below
x= (-b +-sqrtD)/(2a)

Here, D = b^2-4ac

so, if D>0, sqrtD is real and we have two real solutions viz., x= (-b+sqrtD)/(2a) and x=(-b - sqrtD)/(2a)

If D=0, sqrtD=0 and we have one real solution viz., x=(-b)/(2a)

If D<0, sqrtD is imaginary and we have two imaginary solutions viz., x= (-b + i*sqrt|D|)/(2a) and x= (-b - i*sqrt|D|)/(2a)