Two numbers whose sum is 6 and the absolute value of whose difference is 8 are the roots of the equation 

Correct option is (B) x² – 6x – 7 = 0

Let both numbers are a & b.

\(\because\) Their sum = 6

and absolute value of their difference = 8

i.e., a+b = 6  _____________(1)

& a - b = 8    _____________(2)   (Let a > b)

By adding equations (1) & (2), we get

(a+b) + (a - b) = 6+8

\(\Rightarrow\) 2a = 14

\(\Rightarrow\) a = \(\frac{14}2\) = 7

\(\therefore b=6-a\)     (From (1))

\(=6-7=-1\)

\(\therefore\) Product of roots = ab

\(=7\times-1=-7\)

\(\therefore\) Required quadratic equation is

\(x^2-\) (Sum of roots) x + Product of roots = 0

\(\Rightarrow x^2-(a+b)x+ab=0\)

\(\Rightarrow\) \(x^2-6x-7=0\)

Hence, required equation is \(x^2-6x-7=0.\)

Correct option is B) x² – 6x – 7 = 0