Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients 2root 2xsquare - 9x + 5root2​

Answer 1

Solution:-

Given:-

• Polynomial:- 2√2x² - 9x + 5√2

To Find:-

• Two Zeroes of the Polynomial = ?

Find:-

=) 2√2x² - 9x + 5√2

=) 2√2 x² - ( 4 + 5)x + 5√2

=) 2√2x² - 4x - 5x + 5√2

=) 2√2x ( x - √2) - 5 ( x - √2)

=) ( x - √2) ( 2√2x - 5)

=) [ x = √2 ] and

=) x = (5/2√2) × ( 2√2/2√2)

=) x = 10√2 / 8

=) [x = 5√2/4]

Let [ α = √2 ] and [ β = 5√2 /4 ]

Verification:-

• Sum of Zeroes = -b/a

=) α + β = -b/a

=) √2 + 5√2/4 = - (-9)/ 2√2

=) ( 4√2 + 5√2)/4 = ( 9/2√2 ) × ( 2√2/2√2)

=) (9√2)/4 = 18√2/8

=) (9√2)/4 = 9√2 /4

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

• Product of Zeroes = c/a

=) αβ = c/a

=) √2 × 5√2/4 = 5√2 / 2√2

=) 10/4 = 5/2

=) 5/2 = 5/2

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

Hence Verified!

Answer 2

here is the answer

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