Question

if one root of the equation (p2+2)x2+13x+3p is the reciprocal of the other .Find the value of p.

Answer 1

Hope you find it helpful

Answer 2

Hi there !

Let α and $\frac{1}{ \alpha }$ be the zeroes of p[x] .

Product of zeroes = c/a = $\frac{3p}{ p^{2} + 2 }$
     $\frac{3p}{ p^{2} + 2 }$      =  α  ×  $\frac{1}{ \alpha }$
         $\frac{3p}{ p^{2} + 2 }$  = 1

cross multplication :-


p²  + 2 = 3p


p²  -3p + 2 = 0

splitting the middle terms :-

p²  -2p -p + 2 

p [ p - 2 ] - 1 [ p - 2 ]

[ p - 1 ] [ p - 2 ]

value of p :-
 p = 1 , p = 2