Question

Find a quadratic polynomial whose zeros are 2+root 3 and 2-root 3

Answer 1

equation of quadratic is
{x-(2+root3)}{x-(2-root3)}=0

=>x^2-(2+root3+2-root3) x+(2+root3)(2-root3)

=> x^2-4x+1=0

Answer 2

The quadratic polynomial of the $2+\sqrt{3} \text { and } 2-\sqrt{3} \text { is } \bold{x^{2}-4 x+1}$.  

To find:

“Quadratic polynomial” whose zeros are $2+\sqrt{3} \text { and } 2-\sqrt{3}$

Solution:

$[x-(2+\sqrt{3})][x-(2-\sqrt{3})]=0$

$x^{2}-(2+\sqrt{3}+2-\sqrt{3}) x+(2+\sqrt{3})(2-\sqrt{3})$

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

A quadratic polynomial is a polynomial of degree 2. A univariate quadratic polynomial has the form $f(x)=a_{2} x^{2}+a_{1} x+a_{0}$. An equation involving a ‘quadratic polynomial’ is called a quadratic equation.