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Math
Lois Zimmerman

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

answers: 1
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Answer:

Step-by-step explanation:         GIVEN :

Zeroes of Quadratic Polynomial = (3+√5) and (3-√5)

Let α = (3+√5) β = (3-√5)

We know that,

Quadratic Polynomial = x² - (sum of zeroes)x + (product of zeroes)

Sum of zeroes :

=> α + β

=> (3+√5) + (3-√5)

=> 3 + √5 + 3 - √5

=> 6

α + β = 6

Product of zeroes :

=> αβ

=> (3+√5) (3-√5)

=> 3² - (√5)²

=> 9 - 5

=> 4

αβ = 4

Therefore, the Quadratic Polynomial is :

=> x² - (α + β)x + αβ

=> x² - 6x + 4

423
David
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