Question:medium
Two numbers \( x \) and \( y \) have arithmetic mean 9 and geometric mean 4. Then \( x \) and \( y \) are the roots of:
Two numbers \( x \) and \( y \) have arithmetic mean 9 and geometric mean 4. Then \( x \) and \( y \) are the roots of:
Show Hint
The relation \( x^2 - 2(\text{A.M.})x + (\text{G.M.})^2 = 0 \) is a direct shortcut to finding the equation when means are given. It skips the intermediate step of finding the sum and product separately.
Updated On: May 1, 2026
- \( x^2 - 18x - 16 = 0 \)
- \( x^2 - 18x + 16 = 0 \)
- \( x^2 + 18x - 16 = 0 \)
- \( x^2 + 18x + 16 = 0 \)
- \( x^2 - 17x + 16 = 0 \)
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on relationship between a.m. and g.m.
- If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
- CBSE Class XI
- Mathematics
- relationship between a.m. and g.m.
- What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
- CBSE Class XI
- Mathematics
- relationship between a.m. and g.m.
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?
- CBSE Class XI
- Mathematics
- relationship between a.m. and g.m.
- If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A±√(A+G)(A-G).
- CBSE Class XI
- Mathematics
- relationship between a.m. and g.m.
- Want to practice more? Try solving extra ecology questions todayView All Questions
