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If the sum of two roots of the equation X^3 - pX^2 +qX - r = 0 is zero then (1) pq = r (2) qr = p(3) pr = q (3) pqr = 1

If the sum of two roots of the equation X^3 - pX^2 +qX - r = 0 is zero then (1) pq = r (2) qr = p(3) pr = q (3) pqr = 1

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
hence we can say that those two roots will  be opposite sign but equal magnitude.
let those are m, -m
now sum of three roots = p
hence third root will be p
now 
m*(-m) + m*p + (-m)*p = q
hence  –m2 = q
now m*( –m) * p = r
 –m2 p  = r
put value of  –m2 = q
hence  pq = r
hence option A will be correct

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