If the ratio of the roots of the equation x2 – 2ax + b = 0 is equal to that of the roots x2 – 2cx + d = 0, then:
a) a2b = c2 d b) a2c = b2d
b) a2d = c2b d) d2 b = c2 a

• x^2-2ax+b=0 for this eqn..roots r....R1=2a/1,R2=b/1;
  x^2-2cx+d=0 for this eqn ..roots r...R3=2c/1,R4=d;
  As per question ,2a/b=2c/d
  =>2ad=2bc (Option b)ans
• 8 years agoHelpfull: Yes(17) No(10)
• answer is C
  
  roots for 1st equation will be (a+√a^2-b)/a & (a-√a^2-b)/a
  
  similarly for 2nd equation roots will be (c+√c^2-d)/c & (c-√c^2-d)/c
  
  now according to the qsn, ratio of roots are equal, so after solving few steps we will get relation as:
  
  (a+√a^2-b)/(a-√a^2-b) = (c+√c^2-d)/(c-√c^2-d)
  
  now apply Componendo et Dividendo
  
  we will get
  
  a/(√a^2-b) = c/(√c^2-d)
  
  squaring both side,
  
  a^2/(a^2-b) = c^2/(c^2-d)
  
  = a^2c^2 - a^2d = a^2c^2 - bc^2
  
  = a^2d = c^2b -------------- C)
  
• 8 years agoHelpfull: Yes(9) No(5)
• a is right solution
  because a=c,b=d
  hence a2b=c2d
• 8 years agoHelpfull: Yes(3) No(8)
• x = a ab ± 2 – = a ab + 2 – and a ab − 2 –
  and y = c cd ± 2 – = c cd + 2 – and c cd − 2 –
  a ab
  aab
  + −2
  2 – –
  = c cd
  c cd
  + −2
  2 – –
  By reversing componendo and dividendo,
  a
  a b 2 −
  = c
  c d 2 −
  Squaring, a
  a b
  2
  2 – = c
  c d
  2
  2 – , i.e. a2
  d = bc2
• 8 years agoHelpfull: Yes(2) No(2)
• if a = 1, b = 15, the roots for the first equation would be 3 and -5; thus if we make the roots of the second equation -6 and 10 maintaining the -3/5 ratio, we would have c = 2, d = 60. Thus finally a^2 = 1 b = 15 c^2 =4 and d = 60, making b the answer.
• 8 years agoHelpfull: Yes(1) No(5)
• a2d=c2b
  because d and b
  
• 8 years agoHelpfull: Yes(1) No(2)
• let roots of 1st eq. be m,n and roots of 2nd eq. be u,i
  now, sum of roots m+n=-(-2a)/1=>2a and
  sum of roots u+i=-(-2c)/1=>2c
  a/q .....
  m/n=u/i
  m/n+1=u/i+1
  (m+n)/n=(u+i)/i
  2a/n=2c/i
  hence a/c=n/i.....(1)
  also...
  product of roots mn=b
  and ui=d
  as m/n=u/i
  b/n^2=d/i^2
  hence b/d=(n/i)^2.....(2)
  using 1 and 2 we get
  (a/c)^2=b/d
  hence a^2d=c^2b
  so option b is correct
• 7 years agoHelpfull: Yes(1) No(0)
• ans b
  a=c
  c=d
• 8 years agoHelpfull: Yes(0) No(6)
• a=c;
  b=d because
  by equating coefficients
• 8 years agoHelpfull: Yes(0) No(1)
• b
  just solve the equation
• 8 years agoHelpfull: Yes(0) No(2)