Question

Form the quadratic polynomial whose zeros are3+_root 2

Answer 1

Answer:

here is you answer

Step-by-step explanation:

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

)

αβ=9−3

2

+3

2

−2=7 _________ (2)

then

quadratic equation is

x

2

−(α+β)x+αβ=0

From (1) & (2)

[x

2

−6x+7=0]

hope it helps !!!

Answer 2

Question

Form the quadratic polynomial whose zeroes are 3± √2

Answer

Required quadratic equation is

x² - 6x + 7 = 0

Solution

Let us consuder the roots of the required quadratic polynomial be α and β

since the roots were 3±√2

Therefore

α = 3+√2

β = 3 -√2

Now

sum of the roots = 3+√2+3-√2

⇒ α + β = 6

And

product of the roots = (3 + √2)(3-√2)

⇒α×β = 3² -(√2)²

⇒α×β =9 - 2

⇒α×β =7

So the required quadratic equation is

⇒x² - (α+β )x + α×β =0

⇒x² - 6x + 7 = 0