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Let the mean and the variance of seven observations 2, 4, , 8, , 12, 14 , < , be 8 and 16 respectively. Then the quadratic equation whose roots are 3 + 2 and 2 + 1 is :

Options

  1. Ax^2 - 35x + 306 = 0
  2. Bx^2 - 41x + 420 = 0
  3. Cx^2 - 45x + 506 = 0
  4. Dx^2 - 37x + 342 = 0

Correct answer

B. x^2 - 41x + 420 = 0

Step-by-step solution

Given the mean of the seven observations is 8 : 2 + 4 + + 8 + + 12 + 14 7 = 8 40 + + 7 = 8 + = 16 Given the variance of the observations is 16 : x_i^2 n - ( Mean )^2 = 16 2^2 + 4^2 + ^2 + 8^2 + ^2 + 12^2 + 14^2 7 - 8^2 = 16 4 + 16 + ^2 + 64 + ^2 + 144 + 196 7 - 64 = 16 424 + ^2 + ^2 7 = 80 424 + ^2 + ^2 = 560 ^2 + ^2 = 136 Using the identity ( + )^2 = ^2 + ^2 + 2 : 16^2 = 136 + 2 256 = 136 + 2 2 = 120 = 60 Solving for and , they are the roots of the equation t^2 - 16t + 60 = 0 , which are 6 and 10 . Since The roots

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