Prove that both the roots of the equation (x-a)(x-b)=m^2 are always real.

Asked by Ananya | 18th Feb, 2018, 08:14: PM

Expert Answer:

begin mathsize 16px style open parentheses straight x minus straight a close parentheses open parentheses straight x minus straight b close parentheses equals straight m squared
straight x squared minus open parentheses straight a plus straight b close parentheses straight x plus ab equals straight m squared
straight x squared minus open parentheses straight a plus straight b close parentheses straight x plus ab minus straight m squared equals 0
straight D equals open parentheses straight a plus straight b close parentheses squared minus 4 cross times 1 cross times open parentheses ab minus straight m squared close parentheses
straight D equals straight a squared plus 2 ab plus straight b squared minus 4 ab plus 4 straight m squared
straight D equals straight a squared minus 2 ab plus straight b squared plus 4 straight m squared
straight D equals open parentheses straight a minus straight b close parentheses squared plus 4 straight m squared
straight d greater than 0 space as space square space is space always space positive.
Hence comma space roots space of space the space given space quadratic space equation space both space are space real.
end style

Answered by Sneha shidid | 19th Feb, 2018, 10:01: AM