Question

find the quadratic polynomial each with the given number as the zeros of the polynomial 2 +√3 , 2 - 3√3 ​

Answer 1

Zeroes : 2 + √3 , 2 - √3

Sum of the zeroes = 2 + √3 + 2 - √3

==> sum of zeroes = 4 ...(1)

Also,

Product of the zeroes = (2 - √3)(2 + √3)

==> product of zeroes = 2² - (√3)²

==> product of zeroes = 1 ...(2)

We know,

==> p(x) = x² - (sum of zeroes)x + (product of zeroes)

==> p(x) = x² - 4x + 1