Question

7+√​3​​​​,7−√​3​​​​
$7 + \sqrt{3 } \\ 7 - \sqrt{3}$
find the quadratic polynomial whose are zero​

Answer 1

Answer:

x² + 14x + 46

Step-by-step explanation:

It is given that (7 + √3) and (7 - √3) are the two zeroes of the required polynomial.

Let α and β be the zeroes of the required polynomial.

∴ α = 7 + √3, β = 7 - √3

Sum of zeroes = α + β

= 7 + √3 + 7 - √3

= 14

Product of zeroes = αβ

= (7 + √3)(7 - √3)

{ Identity : (a + b)(a - b) = a² - b² }

= (7)² - (√3)²

= 49 - 3

= 46

The required polynomial is :

→ k [ x² + (α + β)x + αβ ]

→ k [ x² + (14)x + 46 ]

Put k = 1, we get

→ x² + 14x + 46