First slide

Theory of equations

Question

The quadratic equation with rational coefficients whose one root is $1 + \sqrt{2}$ is

Easy

A

$x^{2} + 2 x + 1 = 0$
B

$x^{2} - 2 x - 1 = 0$
C

$x^{2} + 2 x - 1 = 0$
D

${(x - 1)}^{2} = 0$

Solution

One root is : $α = 1 + \sqrt{2} β = 1 - \sqrt{2}$
quadratic equation is $x^{2} - (α + β) x + α β = 0$
Required quadratic equation is $x^{2} - 2 x - 1 = 0$

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