Question

write the polynomail whose zeros are 2 +√3 and 2 - √3​

Answer 1

Required Answer:-

Given:

• Zeros of the Quadratic polynomial are 2 + √3 and 2 - √3.

To find:

• The quadratic polynomial.

Solution:

Let α and β be the zeros of the polynomial.

Therefore,

➡ α = 2 + √3

➡ β = 2 - √3

Sum of zeros will be,

= α + β

= 2 + √3 + 2 - √3

= 4

Product of zeros will be,

= αβ

= (2 + √3)(2 - √3)

= (2)² - (√3)²

= 4 - 3

= 1

Therefore,

➡ α + β = 4

➡ αβ = 1

Therefore, the quadratic polynomial will be,

➡ x² - (α + β)x + (αβ) = 0

➡ x² - 4x + 1 = 0

Answer:

• The quadratic polynomial is x² - 4x + 1 = 0

Answer 2

Answer:

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