Question

find the quadratic polynomial whose one zeroes 2+ (square root)3

Answer 1

if one zero is 2+√3 then the other root is 2-√3 .
follow the procedure given below

Answer 2

Answer:

The quadratic polynomial whose one root is $2+\sqrt{3}$ is $x^{2} -4x+1=0$

To find:

The quadratic polynomial whose one root is $2+\sqrt{3}$

Solution:

If one root is $\alpha =2+\sqrt{3}$

Then the second root will be $\beta =2-\sqrt{3}$

Sum of the roots $\alpha +\beta =2+\sqrt{3} +2-\sqrt{3} =4$

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

$=2^{2}-(\sqrt{3})^2=4-3=1$

Hence, the quadratic equation is

$x^2-(Sum of the roots)x+(Products of the roots)$

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

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