Let two numbers have arithmetic mean 9 and geometric mean 4

• Quadratic Equations
• Sequences Series

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

1. x² + 18x + 16 = 0
2. x² - 18x - 16 = 0
3. x² - 18x + 16 = 0
4. x² + 18x - 16 = 0

Solution

Let the two number be a, b

(a+b)/2 = 9 and √(ab) = 4

Required equation: x² - 2(Average value of a, b)x + √(GM)² = 0

The correct option is C.