Question

If one root of the quadratic equation is 2+√3, the equation is __

Answer 1

Answer:

${x}^{2} - 4x + 1 = 0$

Answer 2

Answer:

Quadratic equation is $x^{2} -4x+1=0$

Step-by-step explanation:

Given one root of the quadratic equation is $2+\sqrt{3}$

then the other root will be $2-\sqrt{3}$

Let two root be $\alpha ,\beta$

Sum of the root of a quadratic equation is

               $\alpha+\beta = ( 2+\sqrt{3} )+(2-\sqrt{3})$

            or $\alpha +\beta =4$

 Product of the roots is $\alpha \beta =(2+\sqrt{3}) (2-\sqrt{3})$

                        or $\alpha \beta =2^{2} -(\sqrt{3} )^{2}$

                         or $\alpha \beta =4-3$

                            or $\alpha \beta =1$

So quadratic equation will be

  $x^{2} -$ (sum of the root )x+(product of the roots)=0

or $x^{2} -(\alpha +\beta )x+\alpha \beta =0$

or $x^{2} -4x+1=0$