Q84 / 225 · JEE Main 2004 · Mathematics

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
    $x^2+18 x-16=0$
  • Correct answer
    D
    $x^2-18 x+16=0$

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 $\Rightarrow \quad x^2-18 x+16=0$

Hence, the correct answer is option: 'D'.

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