Question

Maths Assingment - 2
form the polynomial whose zero are :-
2+1 by root 2 and 2-1by root 2


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Answer 1

$\mathfrak{AnSwEr}$

We know that, any polynomial = x^2 - (Sum of the zeroes)x + (Product of the zeroes)

We're provided with the zeroes, we find that:

Sum of zeroes = 4

Product of zeroes = 7/2

Polynomial = x^2 - 4x + 7/2

=》 2x^2 - 8x + 7

Answer 2

Solution:-

Given:-

Zeroes of the Polynomial are [ ( 2 + 1)/√2 ] and [ (2 - 1)/√2 ].

To Find:-

Quadratic Polynomial Equation = ?

Find:-

Let's suppose α + β are the Zeroes of the Polynomial.

We know that,

Quadratic Formula :- x² – (α+β)x +αβ = 0

Now, Finding ( α+β).

=) α+β = [ 2 + 1/√2 ] + [ 2 - 1/√2 ]

=) α+β = [ 2 + 1/√2 + 2 - 1/√2 ]

=) α+β = [ ( 2√2 + 1 + 2√2 - 1)/√2 ]

=) α+β = [ 4√2 /√2 ]

=) α+β = 4.

Now, Finding αβ.

=) αβ = [ 2 + 1/√2 ] × [ 2 - 1/√2 ]

=) αβ = [ 4 -2/√2 + 2/√2 -1/2 ]

=) αβ = [ 4 - 1/2 ] = [ (8-1)/2 ]

=) αβ = 7/2.

Now,

Substituting these value in Quadratic Formula. we get,

=) x² – (α+β)x +αβ = 0

=) x² - 4x + 7/2 = 0

=) (2x² - 8x + 7)/2 = 0

=) 2x² - 8x + 7 = 0