In the question A^B means A raised to the power of B. What is the value of A such that
X^2-11x+A and X^2 -14X +2A will have a common factor?

a) -1/2
b) 24
c) -3
D) 20

• X^2-11x+A
  let it has p and q as roots
  then we can write
  p+q = -(-11)/1 = 11 ....(1)
  p*q = A.....(2)
  
  X^2 -14X +2A
  let it has p and r as the roots
  p+s =14......(3)
  p*s = 2A......(4)
  = 2*p*q, from above equation
  => s = 2q
  
  now (3) => p+2q = 14
  (1)=> 2p+2q = 22
  solving above two
  p = 8
  q = 11 - 8 = 3, from equation (1)
  
  A = p*q = 8*3 = 24 , from equation (2)
  so A = 24
  option b is the answer
  
  
  
  
  
  
  
• 9 years agoHelpfull: Yes(34) No(0)
• due to quadratic equation..... the factor will be like (x-a)(x-b)
  lets assume (x-k) is the common factor the
  x=k is the root of both the eqn
  X^2-11X+A=0 , & X^2-14X+2A=0
  satisfying these two equations we get
  k^2-11k+A=0 ..................................(1)
  k^2-14k+2A=0 ..................................(2)
  on solving we will get
  k=A/3
  substituting this in eq 1 we get A=0 and A= 24
  so A=24 is the answer
• 9 years agoHelpfull: Yes(17) No(0)
• Check the options
  A.-1/2 we get irrational roots, keep it aside
  
  B.24. X*X-11X+24 =(x-3)(x-8). =3,8
  
  X*X-14X+48 =(x-6)(x-8). =6,8
  
  So b.24 is the answer
• 9 years agoHelpfull: Yes(10) No(0)
• X^2-11X+A =0 and X^2-14X+2A=0
  by solving both the equs. , we get,
  x=A/3 (put in any of the above equ.)
  nd get A=24
• 9 years agoHelpfull: Yes(2) No(0)
• b
  the common factor is 8
• 9 years agoHelpfull: Yes(0) No(2)
• ans is b
  x^2-11x+24 x^2-14x+48
  x=12,2 x=6,8
• 9 years agoHelpfull: Yes(0) No(0)