Question

If α and β are the zeros of the polynomial P(x) = 2 − 5 + such that α – β = 1,
find the value of k.

Answer 1

Answer:

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.

Step-by-step explanation:

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