Question

Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`

Answer 1

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