if alpha and beta are the zeroes of the polynomial 3x2+2x+1,find the polynomial whose zeroes are 1-alpha/1+alpha and 1-beta /1+beta
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Answer:
f(x) = 3x²+2x+1
roots are a and b
new zeroes 1-a/1+a and 1-b/1+b
trick : x = 1-a/1+a
x + xa = 1-a
x+ xa - 1 +a = 0
a(x+1) = 1-x
a = 1-x/1+x
now replace x by 1-x/1+x in f(x)
3 (1-x/1+x)² + 2(1-x/1+x) + 1 = 0
x² -2x +3 =0 is the required polynomial.
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@ rakhithakur
f(x) = 3x²+2x+1
roots are a and b
new zeroes 1-a/1+a and 1-b/1+b
trick : x = 1-a/1+a
x + xa = 1-a
x+ xa - 1 +a = 0
a(x+1) = 1-x
a = 1-x/1+x
now replace x by 1-x/1+x in f(x)
3 (1-x/1+x)² + 2(1-x/1+x) + 1 = 0
x² -2x +3 =0 is the required polynomial.
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@ rakhithakur
Answered by
49
.......I hope help you......
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