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Question
Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`
Solution
Let α = `2 + sqrt(7)` and β = `2 - sqrt(7)`
α + β = `2 + sqrt(7) + 2 - sqrt(7)` = 4
and α × β = `(2 + sqrt(7))(2 - sqrt(7))`
= `(2)^2 - (sqrt(7))^2` ......[(a + b)(a – b) = a2 – b2]
= 4 – 7
= – 3
∴ The required quadratic equation is
x2 – (α + β)x + αβ = 0
∴ x2 – 4x – 3 = 0
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