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