If ‘α’ and ‘β’ are the zeroes of the quadratic polynomial $p (x) = x^{2} + 7 x + 5, then (α - β)^{2}$ equals

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Solution

Given that α and β are zeroes of the quadratic polynomial $x^{2} + 7 x + 5.$

∴ α + β = –7 and αβ = 5 …..(ii)

$Now, (α - β)^{2} = α^{2} + β^{2} - 2 α β$

$\Rightarrow (α - β)^{2} = α^{2} + β^{2} + 2 α β - 4 α β$ (Adding and subtracting 2αβ on RHS)

$\Rightarrow (α - β)^{2} = (α + β)^{2} - 4 α β$

$\Rightarrow (α - β)^{2} = (- 7)^{2} - 4 \times 5 = 49 - 20 = 29$ [Using (i)]

Hence, the correct answer is option (a).

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