Question

Find the zero of the polynomial p(X) = 2x^2

2 − (1 + 2√2)x + √2 and

verify the relationship between the zeroes and the coefficients of the

polynomial.​

Answer 1

Que:-

Find the zero of the polynomial p(X) = 2x² − (1 + 2√2)x + √2 and verify the relationship between the zeroes and the coefficients of the polynomial.

Solution:-

Given Quadratic Polynomial Equation:-

• 2x² − (1 + 2√2)x + √2

=) 2x² − (1 + 2√2)x + √2

=) 2x² - x - 2√2x + √2

=) x ( 2x - 1) - √2 ( 2x - 1 )

=) ( 2x - 1) ( x - √2)

=) [ x = 1/2 ] and [ x = √2 ]

Let [ α = 1/2 ] and [ β = √2 ]

Verification:-

• Sum of Zeroes = -b/a

=) α + β = ( 1 + 2√2)/2

=) 1/2 + √2 = ( 1+ 2√2)/2

=) ( 1 + 2√2)/2 = ( 1 + 2√2 )/2

L.H.S. = R.H.S.

• Product of Zeroes = c/a

=) αβ = √2/2

=) 1/2 × √2 = √2/2

=) √2/2 = √2/2

L.H.S = R.H.S

Hence Verified!

Answer 2

Here is ur solution...

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