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Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

If α and ...

Question

If $α$ and $β$ are zeros of the polynomial $2 x^{2} - 4 x + 5$ , find the values of:
$(α - β)^{2}$

A

- 6

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B

1

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C

6

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D

3

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Solution

The correct option is A $- 6$
$(α - β)^{2} = α^{2} + β - 2 α β = (α - + β)^{2} - 4 α β = [(\frac{- (- 4)}{2})]^{2} - 4 \cdot (\frac{5}{2}) = 4 - 10 - 6$

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