Form a quadratic equation whose one root is 3

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Form a quadratic equation whose one root is 3 - √5 and the sum of roots is 6

1. x² − 6x + 4 = 0
2. x² + 6x + 4 = 0
3. x² − 6x − 4 = 0
4. None of these

Correct Option: A

Given : - Sum of the roots ( k₁ + k₂ ) = 6
One root k₁ = 3 - √5
∴ the other root k₂ = 6 - ( 3 - √5) = 3 + √5
∴ Product of roots k₁k₂ = ( 3 - √5 ) ( 3 + √5 )
product of roots = 9 - 5 = 4
Hence , the required equation is x² - (sum of the roots)x + (product of roots) = 0
⇒ x² - 6x + 4 = 0.