Question

Consider the observations: 2, 4, \(\alpha\), \(\beta\), 6, 12, 14. If their mean is 8 and variance = 16, then the quadratic equation whose roots are \(3\alpha + 2\) and \(2\beta + 1\), is

• A. \(x^2 - 49x + 544 = 0\)
• B. \(x^2 - 49x - 544 = 0\)
• C. \(x^2 - 23x - 512 = 0\)
• D. \(x^2 + 23x - 512 = 0\)

Hint:

Variance is the mean of the squares minus the square of the mean. Always calculate \(\alpha + \beta\) and \(\alpha\beta\) to easily find the values of the individual variables.

Answer 1

The Correct Option is A