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Question

# If α and β are the zeroes of the quadratic polynomial f(x)=x2−5x+k such that α−β=1, then the value of k is ___________.

A
6
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B
5
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C
5
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D
6
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Solution

## The correct option is C 6Since α,β are the zeroes of the polynomial, they are also the roots of the equation x2−5x+k=0Sum of the roots =α+β=−b/a=5 →(I)We know from the question that α−β=1 →(II)(I)+(II)⇒2α=6⇒α=3⇒β=2 (by substituting for α in (I))∴αβ=2×3=6 →(III)Produuct of the roots =αβ=c/a=k→(IV)∴k=6 (from (III),(IV))Hence, the answer is option D.

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