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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) $x^{2}-18 x+16=0$
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## 1 Answer

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Answer

(4)

Explanation

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

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