Question

Find the quadratic polynomial whose zeroes are 5/2 and -5/2

Answer 1

If the zeroes are 5/2 and -5/2, then the factors are x-5/2 and x+5/2.
so, the equation is 
=(x-5/2)(x+5/2)
=x^2-5/2x+5/2x-25/4
=x^2-(25/4)

Answer 2

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}x

2

−sum of zeroes+product of zeroes

x² - 10 + 13 is the required polynomial

I Hope this help you