Question

Find the quadratic polynomial whose zeroes are
5 + 2√3 and 5-2√3

Answer 1

Sum of zeroes = 5+2√3 + 5-2√3
= 5 + 5
= 10

product of zeroes = (5+2√3) (5-2√3)
= (5)² - (2√3)²
= 25 - 4×3
= 25-12
= 13


Quadratic polynomial =
${x }^{2} - {sum of zeroes} + {product of zeroes}$
x² - 10 + 13 is the required polynomial.

Answer 2

Hi !

Sum of zeroes = 5+2√3 + 5-2√3
                        = 5 + 5
                       = 10

Product of zeroes = (5+2√3)*(5-2√3)
                             = (5)² - (2√3)²
                             = 25 - 12
                            = 13

A quadratic polynomial is given by :-

x² - (sum of zeros)x + (product of zeros)

x² - 10x + 13  is the required polynomial