Sum of positive roots of the equation $(x^{2} - 12 x + 35) (x^{2} + 10 x + 24) = 0$ is:-

32

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16

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11

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12

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Solution

The correct option is C $12$
$(x^{2} - 12 x + 35) (x^{2} + 10 x + 24) = 0 (x^{2} - 7 x - 5 x + 35) (x^{2} + 6 x + 4 x + 24) = 0 (x (x - 7) - 5 (x - 5)) (x (x + 6) + 4 (x + 6)) = 0 (x - 7) (x - 5) (x + 6) (x + 4) = 0 x = 5, 7, - 6, - 4$
Sum of positive roots is $5 + 7 = 12$

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