If α and β are the zeros of the polynomial f(x) = x^2 - 5x + k such that α- β=1
find the value of k
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Answer:
k=6
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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