Question

X2 - 2x + 3 has two zeroes alpha and beta, find alpha square + beta square
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Answer 1

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Let p(x) = x² - 2x + 3

The zeroes of the polynomial p(x) are α and β

We know that,

Sum of the zeroes = α+β = -b/a

Product of the zeroes = αβ = c/a

Hence in the given case,

α+β = -(-2)/1 = 2

αβ = 3/1 = 3

α² + β²

= (α+β)² - 2αβ

= (2)² - 2×3

= 4 - 6

= -2

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