Find the quadratic equation whose sum of roots is 5 and whose product of roots is 6.

x^{2} + 5 x + 6

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x^{2} - 5 x + 6

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x^{2} + 6 x + 5

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x^{2} - 6 x + 5

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Solution

The correct option is B $x^{2} - 5 x + 6$
Let the quadratic equation be $a x^{2} + b x + c$ = 0 and its roots be $α$ and $β$ .
Now, the sum of roots $α$ + $β$ is 5 and the product of roots $α \times β$ is 6.

From the quadratic equation we know that the sum of its roots is $\frac{- b}{a}$ and the product of roots is $\frac{c}{a}$ .
The value of $\frac{- b}{a}$ = 5 and $\frac{c}{a}$ = 6
On dividing the quadratic equation $a x^{2} + b x + c$ = 0 on both sides by 'a' we get,

$x^{2} + \frac{b}{a} x + \frac{c}{a}$ = 0

Substituting the value of $\frac{b}{a}$ = -5 and $\frac{c}{a}$ = 6,
The equation becomes $x^{2} - 5 x + 6$ = 0.

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