Question

write a polynomial whose zeros are - 2 minus root 3 and 2 minus root 3

Answer 1

Heya !!!


Sum of zeroes = (-2-✓3)+(2-✓3)


=> -✓6



Product of zeroes = ( - ✓3 - ✓2 ) ( -✓3 + 2 )

=> ( -✓3)² - (2)²


=> 3 - 4

=> -1


Therefore,

Required quadratic polynomial = X²-(Sum of zeroes )X + Product of zeroes

=> X² - ( - ✓6 )X + (-1)


=> X² + ✓6X - 1


★ HOPE IT WILL HELP YOU ★

Answer 2

Sum of zeroes = - 2 - √3 + 2 - √3

Sum of zeroes = -√6


Product of zeroes = ( - 2 - √3)(2 - √3)

Product of zeroes = (- √3 - 2)(-√3 + 2)

Product of zeroes = (-√3)² - (2)²

Product of zeroes => 3 - 4 = -1




We know, polynomial = x² - (sum of zeroes)x + product of zeroes 


So, 


Polynomial = x² - (- √6x) - 1

Polynomial = x² + √6x - 1