Question

find a quadratic polynomial one of whose zeros is (3+√2) and the sum of its zeroes is 6.​

Answer 1

Let @ and ß be the zeros of the polynomial

Given that,

One of the zero is 3+√2

i.e.,@=3+√2

and the sum of zeros is 6

i.e.@+ß=6.............[1]

Substituting the value of @ in [1],

→(3+√2)+ß=6

→ß=6-(3+√2)

→ẞ=3-√2

Here,(@,ß)=(3+√2,3-√2)

Now,

Product of zeros:

@ß

=(3+√2)(3-√2)

=3²-√2²

=9-4

=5

★Required Polynomial:

x²-(Sum of zeros)x+Product of zeros

=x²-6x+5