Question

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​

Answer 1

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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Answer 2

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.