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Answers
Step-by-step explanation:
Given Polynomial = x² – 5x + k
And, α – β = 1
Value of k = ??
\rm{ \alpha - \beta = 1 --- (Equation\:I)}α−β=1−−−(EquationI)
According to the relationship between zeros and polynomial's zeros,
\rm{ \alpha + \beta = \dfrac{ - b}{a}}α+β=
a
−b
Where, a is 1 and b is –5.
\rm{\rightarrow{\alpha + \beta = \dfrac{ - ( - 5)}{1}}}→α+β=
1
−(−5)
\rm{\rightarrow{\alpha + \beta = 5}}→α+β=5
\rightarrow{\rm{\alpha =5 - \beta \: --- (Equation \: II)}}→α=5−β−−−(EquationII)
___________________
Substitute equation II in equation I,
\rm{\rightarrow{\alpha - \beta = 1}}→α−β=1
\rm{\rightarrow{(5 - \beta ) - \beta = 1}}→(5−β)−β=1
\rm{\rightarrow{5 - 2\beta = 1}}→5−2β=1
\rm{\rightarrow{ - 2\beta = 1 - 5}}→−2β=1−5
\rm{\rightarrow{ - 2\beta = - 4}}→−2β=−4
\rm{\rightarrow{ \beta = \dfrac{ - 4}{ - 2}}}→β=
−2
−4
\rm{\rightarrow{\beta =2}}→β=2
Answer:
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