if the roots of the equation

Dear Student,

If the roots are equal then the discriminant must be zero.

(-2(ac+bd))² - 4(a²+b²)(c²+d²) = 0

4(ac+bd)² - 4(a²+b²)(c²+d²) = 0

(ac+bd)² = (a²+b²)(c²+d²) 

a²c² + 2abcd + b²d² = a²c² + a²d² + b²c² + b²d² 

2abcd  =  a²d² + b²c²  

a²d² - 2abcd + b²c² = 0   

(ad - bc)² = 0

ad - bc = 0

ad = bc

a/b = c/d

Hence proved.

regards,

Team,

TopperLearning.