If the sum of the zeroes of p(x)=x^2-2(k+1)x+k^2 is 10, what is k?

Correct answer: 4

Use the coefficient relation for a quadratic polynomial. If ax^2+bx+c has zeroes alpha and beta, then alpha+beta=-b/a. In p(x)=x^2-2(k+1)x+k^2, a=1 and b=-2(k+1), so the sum of the zeroes is -[-2(k+1)]/1=2(k+1). The given condition therefore produces 2(k+1)=10. Dividing both sides by 2 gives k+1=5, and subtracting 1 gives k=4. Hence option A is correct. Option B is the intermediate value k+1, not k. Option C results from treating the coefficient as if it were -2k+1, while option D gives a sum of 2(3+1)=8 rather than 10. Substituting k=4 confirms the result: 2(4+1)=10.