Chapter 3.2, Problem 52PFA

To determine

To find: the following function has a zero at 4.

Answer to Problem 52PFA

It is evident from the calculations above that $y=0$ corresponding to $x=4$ for the option D.

Explanation of Solution

Given information:

Given options are,

  $y=3x+4$

  $y=4x-2$

  $2x-y=-4$

  $x-2y=4$

Calculation:

Consider the following equations are,

  $\begin{array}{l}y=3x+\mathrm{4..............}(1)\\ y=4x-\mathrm{2..............}(2)\\ 2x-y=-\mathrm{4.............}(3)\\ x-2y=\mathrm{4...............}(4)\end{array}$

Now, substitute the value of $x$ and solve the equation no (1),

  $\begin{array}{c}y=3x+4\\ y=3\left(4\right)+4\\ y=16\end{array}$

Now, substitute the value of $x$ and solve the equation no (2),

  $\begin{array}{l}y=4x-2\\ y=4\left(4\right)-2\\ y=16-2\\ y=14\end{array}$

Now, substitute the value of $x$ and solve the equation no (3),

  $\begin{array}{c}2x-y=-4\\ 2\left(4\right)-y=-4\\ y=8+4\\ y=12\end{array}$

Now, substitute the value of $x$ and solve the equation no (4),

  $\begin{array}{c}x-2y=4\\ 4-2y=4\\ 2y=0\\ y=0\end{array}$

It is evident from the calculations above that $y=0$ corresponding to $x=4$ for the option D.