# Find the quadratic polynomial whose zeroes are square of the zeroes of the polynomial x2 – x – 1.

et the zeroes of the polynomial x2 – x – 1 be α and β

We have,

and

So,

Now, according to the given condition,

α2 β2 = ( – 1)2 = 1

& (α + β)2 = α2 + β2 + 2 α β

α2 + β2 = (α + β)2 – 2αβ

α2 + β2 = (1)2 – 2( – 1)

α2 + β2 = 3

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

= x2 – (3)x + 1

= x2 – 3x + 1

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