Question

If a ana ß are
are the Zeroes of
x²+px+k
such that a-ß = 1
then find
the value of K?
​

Answer 1

Answer:

1/2

Step-by-step explanation:

x2-px+k

Here, a=1, b=p and c=k

Now, α+ β = -b/a= -(p)/1= -p

α*β = c/a= k

Now,α - β =1

Squaring both sides, we get,

(α - β)^2=12

⇒ α^2 + β^2 - 2αβ = 1

⇒ (α^2 + β^2 + 2αβ) - 4αβ = 1

⇒ (α +β)^2 -4αβ =1

⇒ (-p)2-4k=1

⇒ -4k= 1/(-2p)

⇒ -4k= -2p

⇒ k=1/2 So the value of k is 1/2

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