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Relationship between Zeroes and Coefficients of a Polynomial

If α and β ar...

Question

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

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Solution

Given that $α - β = 1$
$beta plus alpha equals fraction numerator negative left parenthesis negative 5 right parenthesis over denominator 1 end fraction beta plus alpha equals 5........ left parenthesis 1 right parenthesis alpha minus beta equals 1.......... left parenthesis 2 right parenthesis a d d i n g space b o t h space 2 alpha equals 6 alpha equals 3 a l s o space f r o m space e q space 1 beta equals 5 minus 3 beta equals 2 alpha beta equals 2 asterisk times 3 equals 6 a s space w e space k n o w space p r o d u c t space o f space r o o t s space equals k over 1 equals 6 s o space k equals 6$

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