Question

If α and β are the zeroes of the polynomial p(x) = x² + x + 1, find the value of α² + β².

Answer 1

p(x) = x² + x + 1

Product of zeroes = ( constant term ) / (coefficient of x²)

==> ɑβ = 1/1

==> ɑβ = 1 ...(1)

Sum of zeroes = -(coefficient of x) / (coefficient of x² )

==> ɑ + β = -1

Square both sides

==> ɑ² + β² + 2ɑβ = (-1)²

==> ɑ² + β² + 2 = 1 { from (1) , ɑβ = 1 }

==> ɑ² + β² = -1

Answer 2

Answer:

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