If α and β are the zeros of the polynomial f (x) = x² – 5x + k such that α – β = 1, find the value of k​

2 thoughts on “If α and β are the zeros of the polynomial f (x) = x² – 5x + k such that α – β = 1, find the value of k​”

1. Answer:

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   Step-by-step explanation:

   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

   ⇒ (5)2-4k=1

   ⇒ -4k= 7-25

   ⇒ -4k= -24

   ⇒ k=6 So the value of k is 6.

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2. Answer:

   a+ b= 5

   ab=k

   a-b=1

   squaring on both sides

   a²+b²-2ab =1

   (a+b)²-4ab =1

   25-4k =1

   24=4k

   k = 6

   Step-by-step explanation:

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