Question

Let two numbers have A.M as $9$ and G.M. as $4$. Then these numbers are roots of the 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: (B)

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

Let the numbers be $a$ and $b$.
Hence,
$\frac{a+b}{2}=9$
$a+b=18$
And
$\sqrt{ab}=4$
$ab=16$
Hence, the required quadratic equation is
$x^2-18x+16=0$.