Question

find a quadratic polynomial whose zeros are (3+√2) and (3-√2)​

Answer 1

Answer:

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Step-by-step explanation:

let α = 2+3 = 5

and β = 3+2 = 5

→ α+β = 5+5 = 10

and

→ αβ = 5 x 5 = 25

formula for formation of quadratic polynomial → x² - (α+β)x + αβ

→ x² - 10x + 25 , which is the required polynomial

Answer 2

Roots : 3 + √2 , 3 - √2 .

Sum of zeroes = 3 + √2 + 3 - √2 = 6

Product of zeroes = ( 3 + √2 ) ( 3 - √2 ) = 9 - 3√2 + 3√2 - 2 = 7  

Formula : x² - ( sum of roots ) x + product of roots = 0

x² - ( 6 ) x + 7 = 0

Required equation : x² - 6x + 7 = 0