Question

if alfha and beta are the zero of the polynomial x square + 2x +1 ,then 1/alfha + 1/ beta is equal to​

Answer 1

Answer:

$\sf{The \ value \ of \ \dfrac{2}{\alpha}+\dfrac{1}{\beta} \ is \ -2.}$

Given:

$\sf{\alpha \ and \ \beta \ are \ the \ zeroes} \\ \\ \sf{of \ the \ polynomial \ x^{2}+2x+1.}$

To find:

$\sf{The \ value \ of \ \dfrac{1}{\alpha}+\dfrac{1}{\beta}.}$

Solution:

$\sf{The \ given \ polynomial \ is \ x^{2}+2x+1} \\ \\ \sf{Here, \ a=1, \ b=2 \ and \ c=1} \\ \\ \\ \sf{\alpha+\beta=\dfrac{-b}{a}} \\ \\ \sf{\therefore{\alpha+\beta=-2...(1)}} \\ \\ \\ \sf{\alpha\beta=\dfrac{c}{a}} \\ \\ \sf{\therefore{\alpha\beta=1...(2)}} \\ \\ \\ \sf{\leadsto{\dfrac{1}{\alpha}+\dfrac{1}{\beta}}} \\ \\ \sf{\leadsto{\dfrac{\alpha+\beta}{\alpha\beta}}} \\ \\ \sf{From \ (1) \ and \ (2), \ we \ get} \\ \\ \sf{\leadsto{\dfrac{-2}{1}}} \\ \\ \sf{\leadsto{-2}} \\ \\ \\ \purple{\tt{\therefore{The \ value \ of \ \dfrac{1}{\alpha}+\dfrac{1}{\beta} \ is \ -2.}}}$