find the value of p and q if the equation px²+5x+2=0 and 3x²+10x+q=0 have both roots in common.

Asked by ssroul.tcbls | 2nd Jul, 2020, 07:15: PM

Expert Answer:

The given quadratic equations are:
px2+5x+2=0 ... (i)
3x2+10x+q=0 ... (ii)
 
L e t space alpha space a n d space beta space b e space t h e space r o o t s space o f space t h e s e space t w o space q u a d r a t i c space e q u a t i o n s
rightwards double arrow alpha plus beta equals negative 5 over p space space a n d space space alpha beta equals 2 over p
A l s o comma space alpha plus beta equals negative 10 over 3 space space a n d space space alpha beta equals q over 3
rightwards double arrow negative 5 over p equals negative 10 over 3 space space a n d space space 2 over p equals q over 3
rightwards double arrow p equals 3 over 2 space a n d space p q equals 6
rightwards double arrow p equals 3 over 2 space a n d space q equals 6 over p
rightwards double arrow p equals 3 over 2 space a n d space q equals 6 over 3 cross times 2 equals 4
rightwards double arrow p equals 3 over 2 space space a n d space space q equals 4

Answered by Renu Varma | 3rd Jul, 2020, 12:48: PM