Question

It is given that the difference between the zeroes of 4x^2-8kx+9 is 4 and k >0 . Find the value of k.


plz help

Answer 1

Hey

Here is your answer,

Given quadratic equation is 4x2 – 8kx + 9 = 0

Compare with ax2 + bx + c = 0

Hence a = 4, b = – 8k and c = 9

Given difference of two roots = 4

That is α – β = 4 → (1)

Recall that sum of roots of a quadratic equation, (α + β) = –(b/a)

⇒ α + β = – 8k/4 = – 2k
∴ α + β = – 2k → (2)

Product of roots, (αβ) = (c/a)
⇒ αβ = 9/4 → (3)

Recall that (α + β)2 = (α – β)2 + 4αβ
⇒ (– 2k)2 = 42 + 4(9/4)
⇒ 4k2 = 16 + 9 = 25
⇒ k2 = 25/4
∴ k = ± 5/2

Hope it helps you!

Answer 2

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