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

1 Answer
Shiva Reddy
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)#

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