If alpha and beta ate zeroes of x2-5x+k such that alpha+beta=1 find k.

1.	If alpha and beta ate zeroes of x2-5x+k such that alpha+beta=1 find k.
Answer» x2-5x+k\xa0Here, a=1, b=-5 and c=k\xa0Now, α+ β = -b/a= -(-5)/1= 5\xa0α*β = c/a= k/7= k\xa0Now,α -\xa0β =1\xa0Squaring both sides, we get,\xa0(α -\xa0β)2=12\xa0⇒\xa0α2 +\xa0β2 - 2αβ = 1⇒ (α2 +\xa0β2 + 2αβ)\xa0- 4αβ = 1⇒ (α\xa0+β)2 -4αβ =1⇒\xa0(5)2-4k=1⇒\xa0-4k= 7-25\xa0⇒ -4k= -24\xa0⇒\xa0k=6 So the value of k is 6.\xa0

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