Question

If one zero of the polynomial x^2-4x+1 is 2+root 3,write the other zero

Answer 1

Usually if one root is irrational, the other would be the conjugate of it. So, the other root should be 2-root3. If you want to verify, the product should be equal to 1 (c/a) and sum should be equal to -(-4)=4 (b/a). This holds true, so the other root is 2-root3.

Answer 2

Answer:

Hi mate here's your answer

Step-by-step explanation:

Let p( x ) = x² - 4x + 1 ,

compare p( x ) with ax² + bx + c ,

a = 1 , b = -4 , c = 1

one zero = 2 + √3

Let second zero = p

sum of the zeroes = -b/a

p + ( 2 + √3 ) = - ( - 4 )

p = 4 - ( 2 + √3 )

p = 2 - √3

or

product of the zeroes = c/a

( 2 + √3 ) p = 1

p = 1/ ( 2 + √3 )

p = ( 2 - √3 ) / [ ( 2 + √3 ) ( 2 - √3 ) ]

= ( 2 - √3 ) / [ 2² - ( √3 )² ]

= ( 2 - √3 ) / ( 4 - 3 )

= 2 - √3

Therefore ,

required second zero of p( x )

p = 2 - √3

I hope this helps you.

:)