Question

Using formula method,construct the quadratic with the roots(3+root5)(3-root5)

Answer 1

Answer:

x² - 6x + 4 = 0

Step-by-step explanation:

The formula to construct a quadratic equation, when both of the roots are given is x² - (α + β)x + αβ = 0

Given :

α = 3 + √5

β = 3 - √5

Solution :

x² - (3 + √5 + 3 - √5)x + (3 + √5)(3 - √5) = 0

⇒ x² - 6x + (9 - 3√5 + 3√5 - 5) = 0

⇒ x² - 6x + 4 = 0

Hence the answer is x² - 6x + 4 = 0.

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