For what value of k , (4-k)x2 +(2k+4)x +(8k+1) = 0 is a perfect square

 

Asked by agupte28 | 27th Jul, 2019, 05:56: PM

Expert Answer:

left parenthesis 4 minus straight k right parenthesis straight x squared space plus left parenthesis 2 straight k plus 4 right parenthesis straight x space plus left parenthesis 8 straight k plus 1 right parenthesis space equals space 0
for space perfect space square
straight b squared minus 4 ac equals 0
left parenthesis 2 straight k plus 4 right parenthesis squared minus 4 left parenthesis 4 minus straight k right parenthesis left parenthesis 8 straight k plus 1 right parenthesis space equals 0
4 straight k squared plus 16 straight k plus 16 minus 4 open parentheses 32 straight k plus 4 minus 8 straight k squared minus straight k close parentheses equals 0
4 straight k squared plus 16 straight k plus 16 minus 4 open parentheses 31 straight k plus 4 minus 8 straight k squared close parentheses equals 0
4 straight k squared plus 16 straight k plus 16 minus 124 straight k minus 16 plus 32 straight k squared equals 0
36 straight k squared plus 16 straight k minus 124 straight k equals 0
36 straight k squared minus 108 straight k equals 0
36 straight k open parentheses straight k minus 3 close parentheses equals 0
straight k equals 0 comma 3

Answered by Arun | 28th Jul, 2019, 11:53: AM