Question

find a quadratic polynomial whose zeros are 3+ root2 or 3 - root 2

Answer 1

it is given that the roots are 3+_/2 and 3-_/2
Now sum of roots=3+_/2+3-_/2=6
Product of roots =( 3+_/2)(3-_/2)=9-2=7
Now we know that
k {x^2-(sum of roots)x+Product of roots}
k {x^2-6x+7} where k is any non zero constant

Answer 2

let the roots(zeros) be 'a' and 'b'.
therefore, a = 3+√2
b = 3-√2
the formula for quadratic equation:
x^2-(a+b)x+a.b ...........(1)
therefore, putting values of a and b in (1), we get,
x^2-[3+√2-(3-√2)]x+(3+√2).(3-√2)
=>x^2-[3+√2-3+√2]x+(3)^2-(√2)^2
=>x^2-2√2x+(9-2)
therefore, x^2-2√2x+7 is the required quadratic equation