Question

Write a quadratic polynomial whose zeroes are

(√2 + 2)and (√2- 2)​

Answer 1

Step-by-step explanation:

Zeroes of a polynomial represents its roots.

Let α=2+3,β=2−3

Sum of the roots: α+β=2+ 3+2− 3 =4

Product of the roots: αβ=(2+ 3 )(2− 3 )=2 2 −( 3 ) 2 =4−3=1

We know a polynomial can be written as x 2

−(sum of the roots)x+product of the roots=x2−4x+1

Hence the quadratic polynomial is x 2−4x+1