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

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
  1. $x^2+18 x+16=0$
  2. $x^2-18 x-16=0$
  3. $x^2+18 x-16=0$
  4. $x^2-18 x+16=0$

Solution

Let numbers be $a, b \Rightarrow a+b=18, \sqrt{a b}=4 \quad \Rightarrow a b=16, a$ and $b$ are roots of the equation $\Rightarrow \quad x^2-18 x+16=0$

Asked in: JEE Main 2004

Practice more Quadratic Equation questions on Aicharya