Question

if alpha and beta are the zeroes of the polynomial f(x) = x²-5x+k such that alpha - beta =1 , then find the value of 4k​

Answer 1

x² - 5x + k

Here, a = 1, b = -5 and c = k

Now, α + β = $\frac{-b}{a}$ = $\frac{-(-5)}{1}$ = 5

α*β  = c/a= k/7= k

Now,α - β =1

Squaring both sides, we get,

(α - β) = 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

∴ The value of k is 6.

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Answer 2

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