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Question

If α, β are the zeroes of the polynomial f(x)=x25x+k such that αβ=1, find the value of k.

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Solution

Herethegivenequationisx25x+k

Ifweconsiderαandβasrootsoftheequation,then

Sumofzeros,α+β=ba=(5)1=5(1)

Alsoitisgivenαβ=1(2)

Adding(1)and(2)weget

2α=6

α=3

Putα=3in(1),3+β=5

β=2

Nowproductofzeros,αβ=ca=k

Usingvalueofαandβweget

αβ=k

k=32=6

Thusk=6




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