Question
Fri April 13, 2012 By: Asish Joseph
 

if ?(alpha) and ?(beta) are the zeroes of the polynomial x²-4x+3, then form a quadratic polynomial whose zeroes are 2? and 2?.

Expert Reply
Fri April 13, 2012
? and ? are the roots of the quadratic equation x2-4x+3=0
So, sum of roots=-b/a = 4 = ? + ?
 
Product of roots = c/a = 3 = ??
 
New roots are 2? and 2?. New sum of roots =2? +2? = 2(?+?)= 8
New prodcut of roots = 2?x2?=4??=12
 
So the new equation will become
x2-a(sum of roots)x+a(product of roots)=0
 
Or, x2-8x+12=0
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