Question

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

Answer 1

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)`