Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
953 views
in Polynomials by (71.6k points)
closed by
If every pair from among the equations `x^2+px+qr=0,x^2+qx+rp=0 and x^2+rx+pq` has a common root then the product of three common root is (A) pqr (B) 2pqr (C) `p^2q^2r^2`(D) none of these

1 Answer

0 votes
by (71.6k points)
selected by
 
Best answer
Let `alpha, beta` are the roots of `x^2+px+qr = 0.`
Then, `alphabeta = qr ->(1)`
Let `beta, gamma` are the roots of `x^2+qx+rp = 0.`
Then, `betagamma = rp ->(2)`
Let `gamma, alpha` are the roots of `x^2+rx+pq = 0.`
Then, `gammaalpha= pq ->(3)`
Multiplying (1),(2) and (3),
`=> (alphabetagamma)^2 = (pqr)^2`
`=> alphabetagamma = pqr`
So, option `A` is the correct option.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...