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21. If the equations x 2 + ax + b = 0 and x 2 + cx + d = 0 have a common root and the first equation have equal roots, then prove that 2(b + d) = ac

21. If the equations x 2 + ax + b = 0 and x 2 + cx + d = 0 have a common root and the first
equation have equal roots, then prove that 2(b + d) = ac

Grade:12th Pass

1 Answers

rajnish kumar
21 Points
5 years ago
let root of first be p,p. and root of second be p,q.  now. p= -a/2.  p^2=b.. and pq=d p+q=-c. now... take lhs... 2( p^2+ pq). 2(p(p+q)).that is 2(p(-c)).  and also p=-a/2... therefore  lhs get ac. hence prooved

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