1.

Find quadratic polynomial whose zeroes are √2 and 2√2.

Answer»

Let the zeroes of the quadratic polynomial be

α = √2, β = 2√2

Then, α + β = √2 + 2√2 = √2 (1 + 2) = 3√2

αβ = √2× 2√2 = 4

Sum of zeroes = α + β = 3√2

Product of zeroes = αβ = 4

Then, the quadratic polynomial

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

= x2 – (3√2)x + 4

= x2 – 3√2 x + 4


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