Find the sum and product of the roots of the quadratic equation: $x^{2} - 5 x + 8 = 0$

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Solution

We know that for a quadratic equation $a x^{2} + b x + c = 0$ , the sum of the roots is $- \frac{b}{a}$ and the product of the roots is $\frac{c}{a}$ .

Here, the given quadratic equation $x^{2} - 5 x + 8 = 0$ is in the form $a x^{2} + b x + c = 0$ where $a = 1, b = - 5$ and $c = 8$ .

The sum of the roots is $- \frac{b}{a}$ that is:

$- \frac{b}{a} = - \frac{(- 5)}{1} = 5$

The product of the roots is $\frac{c}{a}$ that is:

$\frac{c}{a} = \frac{8}{1} = 8$

Hence, sum of the roots is $5$ and the product of the roots is $8$ .

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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 $x^{2} - 5 x + 5 = 0$ .

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