Question
Sat July 07, 2012 By:

solve the following quadratic equation:

Expert Reply
Mon July 09, 2012
Answer : Given : x2-(5-i)x+(18+i)=0
now , we know here a= 1 , b = i - 5 , c = 18 
D = b2 - 4 ac 
    = ( i-5 )2 - 4 (18+ i)
    = i2 + 52 - 2 ( i ) (5 ) -72 -4i       { using ( a-b)2 = a 2 + b2 - 2ac }
=>D   = -48 -14 i = -2i ( 24 + 7i )
squareroot (D) = i *square root (2) * ( square root (24 + 7i) )
{ applying sqaure root formula of a complex number}
squareroot (D) = i 21/2 ( 1/21/2)( 7 + i) 
                       = 7i -1 or -7i + 1
the two roots will be : (-b + D1/2) /2   and (-b - D1/2) /2    
((5-i) + ( 7i -1) ) /2    and    ((5-i) - ( 7i -1) ) /2
2+ 3i     and 3-4i  are the required two roots Answers
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