Chapter 7.7, Problem 3OE

To determine

Find the sum and product of the roots of the equation $2y^2-y-6=0$ .

Answer to Problem 3OE

The sum of roots is $\frac{1}{2}$ and product of roots is $-3$ .

Explanation of Solution

Given information: The given equation is,

  $2y^2-y-6=0\mathrm{....}\left(1\right)$

Formula used: The sum and product of the roots of an equation of the form $a{x}^2+bx+c=0$ where $a\ne 0$ is given as,

  $\left(\begin{array}{c}\text{Sum of roots}=-\frac{b}{a}\\ \text{Product of roots}=\frac{c}{a}\end{array}\right)\mathrm{....}\left(2\right)$

Calculation: With the help of formula (2) sum and product of roots of (1) is evaluated as,

  $\begin{array}{c}\text{Sum of roots}=-\frac{\left(-1\right)}{\left(2\right)}\mathrm{....}\left(\begin{array}{l}a=2,b=-1\\ \text{and }c=-6\end{array}\right)\\ =\frac{1}{2}\\ \text{Product of roots}=\frac{\left(-6\right)}{\left(2\right)}\mathrm{....}\left(\begin{array}{l}a=2,b=-1\\ \text{and }c=-6\end{array}\right)\\ =-3\end{array}$