Herethegivenequationisx2−5x+k
Ifweconsiderαandβasrootsoftheequation,then
Sumofzeros,α+β=−ba=−(−5)1=5−−−−(1)
Alsoitisgivenα−β=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=3⋅2=6
Thusk=6