Question

if alpha and beta are the zeroes of x^2-1, find a quadratic polynomial whose zeroes are 1/2alpha+beta and 1/2beta+alpha

Answer 1

x²-1=0
x²=1
x=±√1
x=1 or x= -1
alpha=1 and beta= -1
1st zero=1/2×1-1=1×0/2=0
2nd zero=1/2×-1+1=1×0/2=0
so, sum of zeroes =alpha+beta=0+0=0
product of zeroes =alpha×beta=0×0=0
To form a quadratic polynomial
x²+(sum of zeroes)x+product of zeroes =0
x²+0x+0=0
means x²=0
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