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If α and β are the zeros of the polynomial $f x = 5 x 2 − 7 x + 1$ , then find the value of $1 α + 1 β$ .

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answer is C.

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Detailed Solution

Given that α and β are the zeros of the polynomial

f x = 5 x 2 − 7 x + 1

.
For a quadratic polynomial,

p (x) = a x 2 + b x + c

with zeros as

α

and

β

, the relation between the coefficients and the zeros is given as follows,

α + β = − b a α β = c a

So, we have the coefficients as a = 5, b = –7 and c = 1.
Then we have,

α + β = 75 α β = 15

Now, we have to determine

1 α + 1 β

.
We can rewrite after taking the LCM and adding as follows,

1 α + 1 β = β + α α β .......... (i)

Now, substituting the values of

α + β

and

α β

as obtained above, in the equation (i) and simplifying, we get,

1 α + 1 β = 7 / 5 1 / 5 1 α + 1 β = 75 × 51 1 α + 1 β = 7

So, the value of

1 α + 1 β

is obtained as 7.
Hence, the correct option is (3).

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