Question

Write cubic polynomial whose zeroes are 2+√5/2 , 2-√5/2
and 4.

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Answer 1

Hope this helps u

given, three zeros of cubical equation

(2 +√5)/2 , ( 2 -√5)/2 and 4 .

sum of roots = (2 +√5 + 2-√5)/2 + 4 = 6

sum of products of two consecutive roots = ( 2+√5)(2-√5)/4 + (2+√5)/2 ×4 + (2-√5)/2 ×4 = -1/4 + 4 +2√5 +4 -2√5

= 8 -1/4 = 31/4

product of roots = (2+√5)(2-√5)×4/4 = -1

now, equation :-

x³ -(sum of roots )x² + (sum of products of two roots )x - product of roots =0

x³ - 6x² + 31/4x +1 = 0