Question

If alpha and Beta are the zeroes of the polynomial 3x^2+5x +2, find the value of (1/a+1/b).

Answer 1

Heya !!!!


P(X) = 3X² +5X +2


Here,


A = 3 , B = 5 and C = 2




Sum of zeroes = -B/A



Alpha + Beta = -5/3 -------(1)



And,


Product of zeroes = C/A



Alpha × Beta = 2/3 ---------(2)



Therefore,



( 1/ Alpha + 1/Beta )





=> ( Beta + Alpha / Alpha × Beta )





=> (-5/3 / 2/3)





=> -5/2.





HOPE IT WILL HELP YOU........ :-)

Answer 2

Hey there!

If α , β are the zeroes of 3x² + 5x + 2

then ,
α + β = -5/3

αβ = 2/3

$We \: know \: that , \\ \underline{\underline{ If \: ax^2 + bx + c \: is \: a \: quadratic \: polynomial \: in \: x \: whose \: roots \: are \: p, q }}$

$\boxed{Sum \: of \: roots = p + q = \frac{-b}{a} , Product \: of \: roots = p*q = \frac{c}{a} }$

Now,

1/α + 1/β

= β + α / αβ

= -5/3 / 2/3

= -5/2

Therefore, Value of 1/α + 1/β = -5/2