Show that equation 2(a^2+b^2)x^2+2(a+b)x+1=0 ,has no real roots ,when a is not equal to b.

Asked by snisarulhaq | 28th Dec, 2017, 01:56: PM

Expert Answer:

begin mathsize 16px style 2 open parentheses straight a squared plus straight b squared close parentheses straight x squared plus 2 open parentheses straight a plus straight b close parentheses plus 1 equals 0
straight D equals straight B squared minus 4 AC
straight D equals open square brackets 2 open parentheses straight a plus straight b close parentheses close square brackets squared minus 4 cross times 2 open parentheses straight a squared plus straight b squared close parentheses
After space solving space you space will space get space
straight D equals negative 4 open parentheses straight a minus straight b close parentheses squared
As space open parentheses straight a minus straight b close parentheses squared space is space always space positive.
Hence comma space straight D less than 0
The space given space equation space has space no space real space roots. end style

Answered by Sneha shidid | 28th Dec, 2017, 02:25: PM