Find the equation whose sum of roots and product of roots are the product and sum of roots of $x^{2} + 5 x + 6 = 0$ respectively.

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x^{2} - 6 x - 5 = 0

x^{2} - 5 x - 6 = 0

x^{2} + 11 x - 1 = 0

None

answer is A.

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Detailed Solution

Sum of roots of

x^{2} + 5 x + 6 = 0

\frac{- 5}{1} = - 5

.
Product of roots of

x^{2} + 5 x + 6 = 0

\frac{6}{1} = 6

.
Sum of roots of the required equation is equal to 6 and the product of roots of the required equation is equal to −5.
Required quadratic equation is

x^{2} - 6 x - 5 = 0

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