Question

Write the quadratic equation whose one root is 2+√5

Answer 1

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Answer 2

Answer:

The required quadratic equation is $x^2-4x-1=0$

Step-by-step explanation:

Given : One root of quadratic equation is $2+\sqrt{5}$

To find : The quadratic equation

Solution :

we know, if $2+\sqrt{5}$ is one of the root of quadratic equation then,

$x=2+\sqrt{5}$

$x-2=\sqrt{5}$

Squaring both side,

$(x-2)^2=(\sqrt{5})^2$

$x^2+4-4x=5$

$x^2+4-4x-5=0$

$x^2-4x-1=0$

Therefore, The required quadratic equation is $x^2-4x-1=0$.