If the zeroes are 6 + √5 and 6 − √5, what are their sum and product respectively?

Correct answer: 12 and 31

Let α = 6 + √5 and β = 6 − √5. Their sum is α + β = (6 + √5) + (6 − √5) = 12 because the two radical terms cancel. Their product is αβ = (6 + √5)(6 − √5). Using (a+b)(a−b) = a²−b², this becomes 6² − (√5)² = 36 − 5 = 31. Therefore the required sum and product are 12 and 31, respectively, so option A is correct. Option B forgets to subtract 5 from 36. Option C uses only one constant term for the sum, and option D gives the difference of the conjugate numbers rather than their sum. The conjugate structure makes both calculations straightforward.