Question

find a quadratic polynomial whose zeros are 5 + root 3 and 5 minus root 3​

Answer 1

Answer:

x² + 10x + 22

Step-by-step explanation:

Let the zeroes of the polynomial be α and β.

α = 5 + √3 β = 5 - √3

Now,

Sum of zeroes = α + β = (5 + √3) + (5 - √3)

α + β = 10 ...(i)

Product of zeroes = αβ = (5 + √3)(5 - √3)

= (5)² - (√3)²

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

= 25 - 3

αβ = 22 ...(ii)

Now,

The required polynomial is :

= k [ x² + (α + β)x + αβ ]

= k [ x² + (10)x + 22 ]

= k [ x² + 10x + 22 ]

Put k = 1, we get

= x² + 10x + 22