Question

Write the polynomial whose zeros are 2 + root 3 and 2 minus root 3

Answer 1

Dear student,

as we are provided with the two roots, let them be $\alpha$ and $\beta$,
hence $\alpha$ =$2+\sqrt{3}$ & $\beta$ = $2-\sqrt{3}$
let the quadratic equation be ax² + bx + c =0
now, we know, when the roots are given , the quadratic equation can be formed as x² - ​​​($\alpha$ + $\beta$)x + $\alpha$$\beta$ =0
we know,
$\alpha$ + $\beta$ = (2 +$\sqrt{3}$ ) + (2 -$\sqrt{3}$ ) = 4
$\alpha$$\beta$ = (2 +$\sqrt{3}$ )(2 -$\sqrt{3}$ ) = (4 - 3) = 1
so, putting these values in the above equation we get
x² - 4x + 1 = 0
hope you find this useful.