Question

find a quadratic polynomial whose zeroes are 1/2+2√3 and 1/2-2√3

Answer 1

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Zeroes = 1/2+2√3 and 1/2-2√3

Sum of zeroes = 1/2+2√3 + 1/2-2√3
= 1/2 + 1/2
= 1

Product of zeroes = [1/2+2√3] x [1/2-2√3]
= [ 1/2 ] ² - [ 2√3 ]²
= 1/4 - 12
= 1/4 - 12 x 4/4
= 1/4 - 48 / 4
= -47 /4

Quadratic polynomial:-
x² - [ sum of zeroes ]x + [ product of zeroes ]
=x² - x + -47/4


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