Question
Sat July 14, 2012 By:

if alpha,beta are the zeroes of the polynomial x2+10x+30,form a quadratic polynomial whose zeroes are (alpha+2beta)and(2apha+beta)

Expert Reply
Sat July 14, 2012
Alpha + beta = -10/1 = -10
Alpha . beta = 30/1 = 30
 
Now, for the required polynomial:
S = (alpha+2beta) + (2apha+beta) = 3(alpha + beta) = -30
P = (alpha+2beta) . (2apha+beta)
  = 2 alpha square + 5 alpha . beta + 2 beta square
  = 2 (alpha square + beta square) + 5 alpha . beta
  = 2 [(alpha + beta)2 -2 alpha beta)] + 5 alpha . beta
Substitute the values to get P.
 
Thus, required polynomial will be:
x2 - Sx + P
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