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)

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

Given $\frac{a+b}{2}=9;\sqrt{ab}=4$

$\Rightarrow a+b=18;ab=16.$

$\therefore$ Equation with $a,b$ as roots is

$x^2-(a+b)x+ab=0$

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