Question

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

• A. $x^2 + 18x + 16 = 0$
• B. $x^2 −18x −16 = 0$
• C. $x^2 + 18x −16 = 0$
• D. $x^2 −18x + 16 = 0$

Answer 1

Answer: (D)

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