Question

The quadratic polynomial whose zeroes are 2–√2  and −2–√−2  is​

Answer 1

Answer:

x²+2√2x-2=0

Step-by-step explanation:

I think you meant the zeroes as (2–√2)  and (−2–√2) and not as (2–√2)  and (−2–√−2) since (−2–√−2) is not a real number as the root of the number √−2 is imaginary.

So, we will take the zeroes as 2–√2  and −2–√2

For the polynomial ax²+bx+c=0,

Sum of zeroes =(2–√2)+ (−2–√2)

=2–√2−2–√2

= -2√2

=-b/a

Product of zeroes =(2–√2) (−2–√2)

=-(2–√2) (2+√2)

=-(4-2)

=-2

=c/a

For a=1, we have

-b/a= -2√2

b=2√2

and

c/a=-2

c=-2

Hence, one of the polynomials (ax²+bx+c=0) is

x²+2√2x-2=0