If the equation $x^{2} + b x + c = 0$ have roots of opposite sign of the roots of the equation $x^{2} - 5 x + 6 = 0$ then find the values of $b a n d c$ ?

b = 5, c = - 6

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b = - 5, c = 6

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b = - 5, c = - 6

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None of these

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Solution

The correct option is A $b = 5, c = - 6$
$x^{2} - 5 x + 6 = 0 (x - 2) (x - 3) = 0 x = 2, 3 new roots = - 2, - 3 sum = - 5 product = 6 equation : x^{2} - (s u m o f r o o t s) x + p r o d u c t o f r o o t s = 0 ∴ x^{2} + 5 x + 6 = 0 b = 5, c = 6$

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