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 = 
x2−sumofzeroes+productofzeroes{x }^{2} - {sum of zeroes} + {product of zeroes}x2−sumofzeroes+productofzeroes 
x² - 10 + 13 is the required polynomial

Answer 2

roots of the form (x-a)(x-b)