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If the circles described on the line joining the points (0, 1) and $(α, β)$ as diameter cuts the X-axis in points whose abscissae are roots of equation $x^{2} - 5 x + 3 = 0$ then $(α, β)$ $=$

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$(5, 3)$

$(3, 5)$

$(- 5, 3)$

$(- 5, - 3)$

answer is A.

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Detailed Solution

$x^{2} - 5 x + 3 = 0$

Let $x_{1}, x_{2}$ are ab Secissae

$x_{1} + x_{2} = 5, x_{1} x_{2} = 3 (0, 1) (α, β) (x - 0) (x - α) + (y - 1) (y - β) = 0 c = (5, 3)$

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