Question

If α, β are the zeroes of a quadratic polynomial 2x2 – 4x + 1, find the value of
1/(2∝ + β) + 1/(α+2β)

Answer 1

Actually your question has some mistakes

Correct Question

If α, β are the zeroes of a quadratic polynomial 2x^2 – 4x + 1, find the value of

$\dfrac{1}{2∝ + β}$ +$\dfrac{1}{∝ + 2β}$

ANSWER

Given, alpha and beta are zeroes of quadratic polnomial, p(x) = 2x^2 – 4x + 1

Now,

plz refer to the attachment for the answer with full explanation.

Remember

1)Sum of Zeroes

= $\dfrac{-b}{a}$

2)Product of zeroes

=$\dfrac{c}{a}$

3)Identities used=>

-{x+y}^2

= {x}^2 + {y}^2+2xy

Answer 2

Answer:

$\bf\pink{\underline{\underline{\fbox{AnsweR:}}}}$

2x² - 4x +5 =0

α+β = -(-4/2) = 2

αβ = 5/2

i)α² +β² = (α+β)² - 2αβ

             = (2)²- 2×(5/2) = 4-5 

             = -1

ii)(α-β)² = (α+β)² - 4αβ

             =(2)² - 4×(5/2) = 4 - 10

             = -6

Hope it will be helpful :)...✍️