Question

from the quadratic equation whose roots are 2 + √5 and 2 - √5​

Answer 1

Answer:

Let α, β be the given roots.

Then α = 2 + √5 and β = 2 - √5

α + β = 2 + √5 + 2 - √5 = 4

and αβ = (2 + √5)(2 - √5)

⇒ α + β = 4 and αβ = (2)2 - (√5)2

⇒ α + β = 4 and αβ = 4 - 5

⇒ α + β = 4 and αβ = - 1

Required quadratic equation

x2 - (α + β)x + αβ = 0

⇒ x2 – 4x – 1 = 0

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Answer 2

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