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=0ax2+bx+c=0

the solutions for above quadratic equation are as below
x= (-b +-sqrtD)/(2a)x=b±D2a

Here, D = b^2-4acD=b24ac

so, if D>0D>0, sqrtDD is real and we have two real solutions viz., x= (-b+sqrtD)/(2a)x=b+D2a and x=(-b - sqrtD)/(2a)x=bD2a

If D=0D=0, sqrtD=0D=0 and we have one real solution viz., x=(-b)/(2a)x=b2a

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