Chapter 8, Problem 17MCQ

To determine

To Find: Solution of the equation and verify its solution.

Answer to Problem 17MCQ

The solution of the equation $6p^2-3p=0$ are $p=0$ and $p=\frac{1}{2}$

  $p=0$ is a solution of the equation $6p^2-3p=0$

  $p=\frac{1}{2}$ is a solution of the equation $6p^2-3p=0$

Explanation of Solution

Given information:

Equation is $6p^2-3p=0$

Calculation:

Consider the following calculation to find the solution of the equation (1):

  $6p^2-3p=0$

  $3p(2p-1)=0$

  $p=0$ or $p=\frac{1}{2}$ Zero Product Property

  $p=0p=\frac{1}{2}$ Solve each equation

Therefore, the solution of the equation $6p^2-3p=0$ are $p=0$ and $p=\frac{1}{2}$

Substitute $p=0$ in the equation (1) as,

  $0(0-1)=0$

  $0=0$

Thus, $p=0$ is a solution of the equation $6p^2-3p=0$

Substitute $p=\frac{1}{2}$ in the equation (1) as,

  $\begin{array}{cc}2\times \left(\frac{1}{2}\right)-1& =0\\ 0& =0\end{array}$

Thus, $p=\frac{1}{2}$ is a solution of the equation.