Question

find the quadratic polynomial whose zeroes are 2+√3 and 2-√3​

Answer 1

Answer:

{x-(2+√3)}{x-(2-√3)}

x^2-(2+√3+2-√3)x+(2+√3)(2-√3)

x^2-4x+4-3

x^2-4x+1

Answer 2

Answer:

let the zeroes be A and B respectively

A = 2 + √3 ; B = 2 - √3

We know that

Sum of the zeroes (A + B)

=> 2 + √3 + 2 - √3

=> 4

Product of the zeroes (AB)

=> (2 + √3) (2 - √3)

Using (a + b) (a - b) = a² - b²

=> (2)² - (√3)²

=> 4 - 3

=> 1

So , the polynomial p(x) = x² - (A + B)x + AB

=> x² - (4)x + 1

=> x² - 4x + 1