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Definition of Functions

If α and ...

Question

If $α$ and $β$ are the zeros of the polynomial $f (x) = x^{2} - 5 x + k$ such that $α - β = 1$ , the value of $k$ is

A

12

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B

6

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C

4

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D

1

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Solution

The correct option is B $6$
$α + β = 5$
$α β = k$
$α - β = 1$
$(α - β)^{2} = 1$
$(α + β)^{2} - 4 α β = 1$
$25 - 4 k = 1$
$24 = 4 k$
$k = 6$

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