Q. Let the 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) $x^{2} + 18x + 16 = 0$
Explanation
(b)
Let the two numbers are $x_{1}$and $x_{2}$
Given, $\frac{x_{1} + x_{2}}{2} = 9$ and $x_{1}.x_{2} = 16$
$\Rightarrow \ \ x_{1} + x_{2} = 18$ and $x_{1}.x_{2} = 16$
Hence, required equation is
$x^{2} -$(sum of roots)$x +$product of roots=0
$\Rightarrow x^{2} - 18x + 16 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.