Question

If roots of euation (a square +b square) x square +2(bc-ad)x+ c square +d square=0 if roots are real and equal show ac+bd=0

Answer 1

Answer:

Since the roots are real and equal, the discriminant must be zero.

The discriminant here is

( 2( bc - ad) )²  -  4 ( a² + b² ) ( c² + d² )

= 4 ( b²c² + a²d² - 2abcd ) - 4 ( a²c² + a²d² + b²c² + b²d² )

= - 4 ( a²c² + b²d² + 2abcd )

= -4 ( ac + bd )²

So this must be zero, and so

ac = bd = 0