Question

form the polynomial whose zeroes are
$2 + \frac{1}{ \sqrt{2} }$
and
$2 - \frac{1}{ \sqrt{2} }$
​

Answer 1

Answer:

answer for the given problem is given

Answer 2

$\sf\underbrace{\red{SOLUTION:-}}$

✪ The form of polynomial Equation is ,

$\checkmark\:\bf{\underline{\purple{\boxed{x^2\:-(sum\:of\:roots)x\:+(product\:of\:roots)\:=\:0\:}}}}$

GIVEN :-

• two roots are,

1. $\rm{(2\:+\:{\dfrac{1}{\sqrt{2}}})\:}$
2. $\rm{(2\:-\:{\dfrac{1}{\sqrt{2}}})\:}$

CALCULATION :-

(✧) Sum of roots is,

$\rm{\:=\:2\:+\:\dfrac{1}{\sqrt{2}}\:+\:2\:-\:\dfrac{1}{\sqrt{2}}\:}$

$\rm{\:=\:4\:}$

(✧) Products of roots is,

$= (2 + \frac{1}{ \sqrt{2} } ) \times (2 - \frac{1}{ \sqrt{2} } ) \\ \\ = 4 - \frac{1}{2} \\ \\ = \frac{7}{2}$

☞ So, the polynomial form is,

$\rm{x^2\:-\:(4)x\:+\:\dfrac{7}{2}\:=\:0\:}$

$\bigstar\:\rm{\underline{\green{\boxed{2x^2\:-\:8x\:+\:7\:=\:0\:}}}}$