Question

it is given that the difference between the zeroes of 4x^2-8kx+9 is 4.find the value of k​

Answer 1

Answer:

Here is ur answer bro

$Given quadratic equation is 4x2−8kx+9=0</p><p></p><p></p><p>Comparing with ax2+bx+c=0</p><p></p><p></p><p>we get a=4b=−8xc=9</p><p></p><p></p><p>Difference of two roots is =4</p><p></p><p></p><p>Let α,β be the roots</p><p></p><p></p><p>α−β=4→(1)</p><p></p><p></p><p>Sum of roots ⇒α+β=48k=2k</p><p></p><p></p><p>Product of roots ⇒αβ=49</p><p></p><p></p><p>Now (α+β)2=(α−β)2+4αβ</p><p></p><p></p><p>(2k)2=(4)2+4×49</p><p></p><p></p><p>4k2=16+9</p><p></p><p></p><p>k2=425</p><p></p><p></p><p>⇒k=25 or −25</p><p></p><p>$

Answer 2

Step-by-step explanation:

Brainly User

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

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