Question

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

Answer 1

Given zeroes,
5+√2 and 5-√2(z1 and z2)

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

Product of zeroes=(5+√2)(5-√2)
Product of zeroes=25-2=23

We know that quadratic polynomial is in the form of,
=ax²-bx+c

we also know
sum of zeroes = -b /a
product of zeroes = c/a


So
-b/a =10 and c/a = 23
taking a=1 we get
b= -10
c= 23


Hence x²-10x+23 is the required polynomial.