Find a quadratic polynomial whose zeroes are 3 = root 5 and 3- root 5.
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the quadratic polynomial with zeroes α and β
x² - (α +β) +αβ
= x² - ( 3 +√5 + (3- √5))x + (3+√5)(3-√5)
= x² - 6x + (3² - (√5)²)
= x² -6x + (9 - 5)
= x²- 6x +4
x² - (α +β) +αβ
= x² - ( 3 +√5 + (3- √5))x + (3+√5)(3-√5)
= x² - 6x + (3² - (√5)²)
= x² -6x + (9 - 5)
= x²- 6x +4
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