Question

find a quadratic polynomial whose zeros are 2+underroot3 and 2-underroot 3

Answer 1

we know that quadratic polynomial= x^2 -( sum of zeros * x ) + products of zeroes

sum of zeroes= 2+ root 3 +2 -root 3
=2+2 +root3 - root 3
= 4

product of zeros = (2 + root 3) (2 - root 3)

by using a^2-b^2= (a+b) ( a-b)

product of zeros become = 2^2 - root 3^2
= 4-3
= 1
now the polynomial
,
= x^2 - 4x + 1