Problem: If the arithmetic mean of two numbers is 6 and their geometric mean is 10, then an equation with the given two numbers as roots is:
Answer Choices:
A. x2+12x+100=0
B. x2+6x+100=0
C. x2−12x−10=0
D. x2−12x+100=0
E. x2−6x+100=0
Solution:
Let r and s be the roots of the required equation. Since 6=2r+s,r+s=12 and since 10=rs, rs=100, so that, in the required equation, the sum of the roots is 12 and the product of the roots is 100. Hence, x2−12x+100=0.