Find quadratic polynomial whose zeroes are 3 + √7 and 3 - √7.

1.	Find quadratic polynomial whose zeroes are 3 + √7 and 3 - √7.
Answer» Let the zeroes of the quadratic polynomial be α = 3 + √7, β = 3 – √7 Then, α + β = 3 + √7 + 3 – √7 = 6 αβ = (3 + √(7)) × (3 – √7) = 9 – 7 = 2 Sum of zeroes = α + β = 6 Product of zeroes = αβ = 2 Then, the quadratic polynomial = x² – (sum of zeroes)x + product of zeroes = x² – (6)x + 2 = x² – 6x + 2

Answer»

Let the zeroes of the quadratic polynomial be

α = 3 + √7, β = 3 – √7

Then, α + β = 3 + √7 + 3 – √7 = 6

αβ = (3 + √(7)) × (3 – √7) = 9 – 7 = 2

Sum of zeroes = α + β = 6

Product of zeroes = αβ = 2

Then, the quadratic polynomial

= x² – (sum of zeroes)x + product of zeroes

= x² – (6)x + 2

= x² – 6x + 2

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