Question

If one root of the equation $l{x}^2+mx+n=0$ is $\frac{9}{2}$ $(l,m$ and n are positive integers) and $\frac{m}{4n}=\frac{l}{m},$ then $\frac{1}{x}+\frac{1}{y}$ is equal to

• A. 80
• B. 85
• C. 90
• D. 95
• E. 100

Answer 1

Answer: (B)

Given, $l{x}^2+mx+n=0$ ...(i) Now, $D=m^2-4ln$
$=0$ ( $\because$ $m^2=4ln$ given)
It means roots of given equation are equal.
$\therefore$ ${\left(x-\frac{9}{2}\right)}^2=0$
$\Rightarrow$ $4x^2+81-36x=0$ ...(ii)
On comparing Eqs. (i) and (ii), we get
$l=4,m=-36,n=81$
$\therefore$ $l+n=4+81=85$