Question

find the zeros of the polynomial 2x^2-(1+2root2)x+root 2 and verify the relationship b/w the zeros and coefficient of the polynomial

Answer 1

1) 2s2 - (1 + 2√2) s + √2 = 2s2 - s - 2√2s + √2= S(2s - 1) - √2(2s - 1) = (2s - 1)(s - √2)

2s - 1 = 0 ⇒ s = 1/2

s - √2 = 0 ⇒ s = √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.

Answer 2

I answered in the above picture