Question

Find a quadratic polynomial whose zeroes are



3 + √2 3 − √2
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Answer 1

Answer:

α=3+√2, β=3-√2

Quadratic polynomial

=x²-(α+β)x+αβ

=x²-(3+√2+3-√2)x+(3+√2)(3-√2)

=x²-(3+3+√2-√2)x+(3)²-(√2)²

=x²-6x-9-2

=x²-6x-11

Answer 2

Answer:

Given zeros of polynomial are 3± 2

Let α,β be zeros of polynomial

then

α+β=3+ 2 +3− 2 =6 ________ (1)

& αβ(3+ 2 )(3−2 )

β=9−3 2 +32 −2=7 _________ (2)

then

quadratic equation is

x 2 −(α+β)x+αβ=0

From (1) & (2)

[x 2 −6x+7=0]