Question

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

Answer 1

$<b>Answer :</b>$

x² - 4x + 1



$<b>Step-by-step explaination :</b>$

Let,

$\alpha$ = 2 + √3 and $\beta$ = 2 - √3

Sum of zeroes, $\alpha$ + $\beta$ –

= 2 + √3 + 2 - √3

= 4

Product of zeroes, $\alpha \beta$ –

= ( 2 + √3 ) ( 2 - √3 )

$<b>( a + b ) ( a - b ) = a² - b²</b>$

= ( 2 )² - ( √3 )²

= 4 - 3

= 1

The required polynomial is –

= x² - ( $\alpha$ + $\beta$ ) x + ( $\alpha \beta$ )

= x² - ( 4 ) x + 1

= $<b><u>x² - 4x + 1</b></u>$

Answer 2

Answer:

x^2 - 4x + 1

Step-by-step explanation:

In the attachment.. Hope it's helpful..