Question

find the quadratic equation, if one of the roots is 2-√5

Answer 1

Heya!!!

Answer to your question:

Quadratic equations occur in pairs.

If one root is 2-sqrt5, other root will be 2+sqrt5.

Sum of roots= 4

Product of roots= (2- sqrt 5)(2+ sqrt5)

=4-5=-1

Equation=>

x^2-(sum)x+product=0

x^2-4x-1=0

Hope it helps ^_^

Answer 2

$\underline{\underline{\bold{Question:}}}$

Find the quadratic equation, if one of the roots is 2-√5 .

$\underline{\bold{Solution:}}$

Given :

• One root of the equation  $\bold{=2-\sqrt{5}. }$

So

• Second root of the equation $\bold{=2+\sqrt{5}. }$

We know that ,

$\boxed{\bold{Standard\:form\:of\:quadratic\:equation=x^{2}-(sum\:of\:roots)x+product\:of\:roots. }}$

$\implies{\bold{x^{2}-(2-\sqrt{5}+2+\sqrt{5})x+(2-\sqrt{5})(2+\sqrt{5}) }}\\\\\\\implies{\bold{x^{2}-4x+(2)^2-(\sqrt{5})^2}}\\\\\\\implies{\bold{x^{2}-4x-1}}\\\\\\\boxed{\boxed{\bold{Equation=x^{2}-4x-1.}}}$