Question

is alpha and beta are the zeros of the polynomial 6 Y squared minus y + 2 find a quadratic polynomial whose zeros are 1 by Alpha Plus One by beta

Answer 1

Answer:

2Y² - Y + 6

Step-by-step explanation:

6Y² - Y + 2

α & β are Zeros

α + β = - (-1)/6 = 1/6

αβ = 2/6 = 1/3

1/α  & 1/β    are roots

so polynomial would be

( Y - 1/α)(Y - 1/β )

= Y² - Y ( 1/α + 1/β)  + 1/αβ

αβ = 1/3

1/α + 1/β = (β + α)/αβ

=>1/α + 1/β = (1/6)/(1/3) = 1/2

Y² - Y (1/2) + 1/(1/3)

Y² - Y (1/2) + 3

multiplying by 2

2Y² - Y + 6

Answer 2

hope it helps

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