Question

It is given that the difference between the zeros of 4x2-8kx+9 is 4 and k>0. then k =?

Answer 1

Hey user here is your answer....

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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)

◆◆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)

● (α + β)2 = (α – β)2 + 4αβ
⇒ (– 2k)2 = 42 + 4(9/4)
⇒ 4k2 = 16 + 9 = 25
⇒ k2 = 25/4
∴ k = +5/2 &-5/2

⭐️Hope it helps you⭐️

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#Rohan ( Maths aryabhatta )

Answer 2

Hope it will be helpful to you