Find the quadratic polynomial if two zeroes are (2+√2) and (2-√2)

1.	Find the quadratic polynomial if two zeroes are (2+√2) and (2-√2)
Answer» Let zeroes be α=(2+√2) and β=(2-√2).Hence, α+β=(2+√2+2-√2) =4And, αβ = (2+√2)(2-√2) ={(2)^2-(√2)^2} = 4-2 = 2Therefore, quadratic polynomial = (x-α)(x-β)= x^2 -(α+β)x + αβ .......(I) On putting the value of (α+β) and αβ in equation (I) we get, quadratic polynomial = x^2 - 4x + 2

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