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.

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

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

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

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None of the above

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Solution

The correct option is A $x^{2} - 6 x - 5 = 0$
In the given equation
sum of roots $= - 5$ and product of roots $= 6$
The standard form of a quadratic equation is: $x^{2} - (S) x + P = 0$ , where S and P are sum and product of roots.
So according to question
$x^{2} - (6) x + (- 5) = 0$
The required equation will be $x^{2} - 6 x - 5 = 0$

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If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation can be $x^{2} - 5 x + 5 = 0$ .

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

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

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

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

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

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