Question

Find a quadratic polynomial with zeros 3+_/2 and 3 - _/2

Answer 1

P(X) = X^2 - (3+_/2+3-_/2) X + (3+_/2)(3-_/2)
=. X^2 - 6X + ( 3^2 - (_/2)^2
= X^2 - 6X + 9 - 2
= X^2 - 6X + 7

Answer 2

Answer:

Sum of zeroes :

$3 + \sqrt{2} + 3 - \sqrt{2} = 6$

Product of zeroes :

$(3 + \sqrt{2} )(3 - \sqrt{2} ) = 7$

Polynomial = $x^2 - 6x + 7$