Let two numbers have arithmetic mean 9 and geometric mean 4.... | MATH - RELATION BETWEEN A.P., G.P. AND H.P | SolveeIt | Solveeit

Today, August 18

Question

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

A

$x ^ { 2 } - 18 x - 16 = 0$

B

$x ^ { 2 } - 18 x + 16 = 0$

C

$x ^ { 2 } + 18 x - 16 = 0$

D

$x ^ { 2 } + 18 x + 16 = 0$

Answer

$x ^ { 2 } - 18 x + 16 = 0$

Explanation

Solution

A = 9, G = 4 are respectively the A.M. and G.M. between two numbers, then the quadratic equation having its roots as the two numbers, is given by $x ^ { 2 } - 2 A x + G ^ { 2 } = 0$ i.e.

$x ^ { 2 } - 18 x + 16 = 0$