Question

a and B are the zeroes of the polynomial f(x) = x² - 5 x + k such that a - B = 1, then
show that k=6
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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

a² + b² –2ab = 1

(a2 + b² + 2ab) –4ab = 1

(a + b)²–4ab = 1

(5)²–4k = 1

⇒ –4k = 7 – 25

⇒ –4k = –24

⇒ k = 6 So the value of k is 6