Question

Find the sum and product of the roots of the quadratic equation: $p{r}^2=r-5$

Answer 1

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

Here, the given quadratic equation $p{r}^2=r-5$ can be rewritten as $p{r}^2-r+5=0$ is in the form $a{x}^2+bx+c=0$ where $a=p,b=-1$ and $c=5$.

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

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

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

$\frac{c}{a}=\frac{5}{p}$

Hence, sum of the roots is $\frac{1}{p}$ and the product of the roots is $\frac{5}{p}$.