Question

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

Answer 1

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

We have,

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

So, the quadratic polynomial

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

= x² – (3)x + 1

= x² – 3x + 1