Question

find quadratic polynomial whose zeros are 5 + 2 root 3 and 5 minus 2 root 3

Answer 1

Hi friend,

(5+2✓3) and (5-2✓3) are the zeros of the polynomial.

let Alpha =(5+2✓3) and Beta =(5-2✓3)

Sum of zeros = (Alpha + Beta) = (5+2✓3) + (5-2✓3) = 10

Product of zeros = (Alpha × Beta) = (5+2✓3)(5-2✓3) = (5)² - (2✓3)² = 25-12 = 13

Therefore,

The required polynomial = X²-(Alpha+Beta)X+Alpha×Beta

=> X²-(10)X+13

=> X²-10X+13

Hence,

The polynomial = X²-10X+13.


HOPE IT WILL HELP YOU.... :-)

Answer 2

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