Question

if alpha and beta are zeros of the f(x) =x squared -5x+k,such that alpha-beta =1,find the value of k

Answer 1

x2-5x+k

 Here, a=1, b=-5 and c=k 

Now, α+ β = -b/a= -(-5)/1= 5 

α*β  = c/a= k/7= k

 Now,α - β =1

 Squaring both sides, we get,

 (α - β)2=12 

⇒ α2 + β2 - 2αβ = 1

⇒ (α2 + β2 + 2αβ) - 4αβ = 1

⇒ (α +β)2 -4αβ =1