0

Guest

Courses New

if every pair of the equation x^2+px+qr=0 , x^2+qx+rp=0 , x^2+rx+pq=0 have a non zero common root then the sum of three common is ?

if every pair of the equation x^2+px+qr=0 , x^2+qx+rp=0 , x^2+rx+pq=0 have a non zero common root then the sum of three common is ?

Grade:11

3 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
7 years ago
243-1613_capture.PNG
Vikas TU
14149 Points
7 years ago
let a be the common root then satifying the root in all the three eqns. we get,
a^2 + ap + qr = 0
a^2 + aq + rp = 0
a^2 + ar + pq = 0
solving all three one by one by elimination method,
we get
a = r with p = q
a = p with q = r
a = q with p = r
Hence, sum of common root => p + q + r 
                                            => 3p = 3q = 3r respectively.
mycroft holmes
272 Points
7 years ago
Sourabh’s answer can be taken a bit further. Note that we have concluded that r is a root of the 1st quadratic i.e. x2+px+qr = 0. From product of roots, the other root is q. Sum of roots gives q+r = -p, or p+q+r = 0.
 
So, the sum of the common roots is 0

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More