Question

If the difference of the zeroes of the polynomial P (x) = 4x²-4 kx + 9 is 4, find the value of 'k'.​

Answer 1

$\bf\large\underline\green{Solution :-}$

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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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