Question

Find the quadratic polynomial whose zeroes are 3 + √5 and 3 - √5.

Answer 1

Answer:

The quadratic polynomial is x² - 6x + 4

Step-by-step explanation:

Sum of zeroes = 3 + √5 + 3 - √5 = 6

Product of zeroes = ( 3 + √5 )( 3 - √5 ) = 3² - ( √5 )² = 9 - 5 = 4

Quadratic polynomial = k{ x² - ( Sum of zeroes )x + Product of zeroes }

Where k ≠ 1

= k( x² - 6x + 4 )

When k = 1

= 1( x² - 6x + 4 )

= x² - 6x + 4

Therefore the quadratic polynomial is x² - 6x + 4