Math, asked by Chaudharivishwa, 2 months ago

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Answered by llItzDishantll
2

Answer:

1) 2x2 - (1 + 2√2) x + √2 = 2x2 - x - 2√2x + √2= x(2x - 1) - √2(2x - 1) = (2x - 1)(x - √2)

2x - 1 = 0 ⇒ x = 1/2

x - √2 = 0 ⇒ x = √2

Therefore, Zeroes of the polynomial are 1/2 and √2.

If α and β are the zeroes of the quadratic polynomial ax2 + bx + c, then

α +β = − b/a

αβ = c/a.

Therefore, sum of the roots is (1 + 2√2) / 2 i.e. (1/2 + √2)

Product of the roots is √2 / 2 = 1/√2.

hence proved.

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