Question

find a quadratic polynomial whose zeroes are 2+√3 and 2-√3​

Answer 1

Answer:

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Answer 2

Solution :

(2 + √3) and (2 - √3) are the zeroes of the quadratic polynomial

Let α and β be the zeroes of the polynomial

Therefore

• α = 2 + √3
• β = 2 - √3

Sum of zeroes = α + β = 2 + √3 + (2 - √3) = 2 + √3 + 2 - √3 = 4

Product of zeroes = αβ = (2 +√3)(2 - √3) = 2² - (√3)² = 4 - 3 = 1

Quadratic polyinomial ax² + bx + c = k[ x² - (α + β)x + αβ ]

[ Where k ≠ 0 ]

Substituting the values

= k( x² - 4x + 1 )

When k = 1

= 1(x² - 4x + 1)

= x² - 4x + 1

Hence, x² - 4x + 1 is a quadratic polynomial whose zeroes are (2 + √3) and (2 - √3).