Find the common root of $x^{2} - 8 x + 15 = 0 x^{2} - 12 x + 35 = 0$

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Solution

$x^{2} - 8 x + 15 = 0 x^{2} - 3 x - 5 x + 15 = 0 x (x - 3) - 5 (x - 3) = 0 (x - 3) (x - 5) = 0 x = 5, 3 x^{2} - 12 x + 35 = 0 x^{2} - 5 x - 7 x + 35 = 0 x (x - 5) - 7 (x - 5) = 0 (x - 7) (x - 5) = 0 x = 7, 5$
So the common root is $x = 5$

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