Question

form the polynomial whose zeroes are 2+1/√2,2-1/√ 2​

Answer 1

$\huge{\underline{\underline{\sf{\pink{Answer:-}}}}}$

the zeroes are are 2+1/√2,2-1/√ 2

sum of the zeroes,

$(2 + \frac{1}{ \sqrt{2} } ) + (2 - \frac{1}{ \sqrt{2} } )$

$= 2 + \frac{1}{ \sqrt{2} } + 2 - \frac{1}{ \sqrt{2} }$

$= 2 + 2 + \frac{1}{ \sqrt{2} } - \frac{1}{ \sqrt{2} }$

$= 4$

product of the zeroes,

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

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

$= 2(2).2( \frac{1}{ \sqrt{2} } ) + \frac{1}{ \sqrt{2} } (2) - \frac{1}{ \sqrt{2} } ( \frac{1}{ \sqrt{2} } )$

$= 4 - \frac{2}{ \sqrt{2} } + \frac{2}{ \sqrt{2} } - \frac{1}{2}$

$= 4 - \frac{1}{2}$

$= \frac{8 - 1}{2}$

$= \frac{7}{2}$

the required polynomial→ x^2-(sum of the zeroes)x+product of the zeroes

$⟹ {x}^{2} - 4x + \frac{7}{2}$

$⟹2 {x}^{2} + 8x + 7$