Question

5) If one root of a equation is 2 +√5,
then the quadratic equation is :​

Answer 1

Step-by-step explanation:

Imaginary roots always comes in pair ( They are conjugate )

So if one root of quadratic is 2+√5 then other must be 2 - √5 .

So roots of quadratic are

$\alpha = 2 + \sqrt{5} \: \: and \: \: \beta = 2 - \sqrt{5}$

Now quadratic

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ {x}^{2} - (2 + \sqrt{5} + 2 - \sqrt{5} ) + (2 + \sqrt{5}) (2 - \sqrt{5} ) = 0 \\ \\ {x}^{2} - 4x + ( {2}^{2} - { \sqrt{5} }^{2} ) = 0 \\ \\ {x}^{2} - 4x - 1 = 0$