Question

If a and B are the zeros of the polynomial f(x) = r -5x + k such that a-B = 1,
find the value of k.
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Answer 1

Answer:

r-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. 

Hope this is helpful