Question

if l and m are the zeroes of x^2+5x+5, find the value of l^-1 +m^-1.​

Answer 1

Given: l and m are the zeroes of $x^2+5x+5$

To find: The value of $l^{-1} +m^{-1}$

Step-by-step explanation:

As we know

$ax^2+bx+c$  is the general quadratic polynomial

and if $\alpha \text { and } \beta$ are the zeroes then

$\alpha + \beta = \dfrac{-b}{a} \\\\ \alpha \beta =\dfrac{c}{a}$

Therefore for  $x^2+5x+5$ we have a= 1 , b= 5 , c= 5

Given l and m two zeroes

$l+m = \dfrac{-b}{a} =-5$

$l+ m = \dfrac{c}{a} =5$

So we have

$l^{-1} +m^{-1}= \dfrac{1}{l} +\dfrac{1}{m} =\dfrac{l+m}{lm}=\dfrac{-5}{5} =-1$

Hence the value of $l^{-1} +m^{-1}$ is -1