Question

Qs 4 (1) - i]
Solve the above question
Step by step

Answer 1

Answer:

x² + 8x + 12 = 0

Step-by-step explanation:

Difference between the roots of a quadratic equation is 4.

α - β = 4    --- (i)

Difference between the cubes of those roots is 208

α³ - β³ = 208     ---- (ii)

On cubing (i), we get

(α - β)³ = 4³

⇒ α³ - β³ - 3αβ(α - β) = 64

⇒ 208 - 3αβ(4) = 64

⇒ αβ = 12

Once again Squaring (i), we get

(α - β)² = 4²

⇒ α² + β² + 2αβ = 16

⇒ α² + β² + 2(12) = 16

⇒ α² + β² = 40

[∴(a + b)² = a² + b² + 2ab]

⇒ (α + β)² = α² + β² + 2αβ

⇒ (α + β)² = 40 + 2(12)

⇒ α + β = 8

The sum of the zeros is 8.

The quadratic equation form is :

x² + (a + b)x + ab = 0

⇒ x² + 8x + 12 = 0

Therefore,

Required Equation = x² + 8x + 12 = 0

Hope it helps!

Answer 2

Step-by-step explanation:

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