Chapter 3.3, Problem 7QR

To determine

To calculate: The positive roots of the given equation. Also, evaluate the function $y=500x^6$ at each root.

Answer to Problem 7QR

The required roots of are 1.173, 2.394 and the values of $y=500x^6$ are 1305 and 94212.

Explanation of Solution

Given information:

The equation: $2x^3-5x^2-2x+6=0$

Calculation:

The given equation is $2x^3-5x^2-2x+6=0$ .

To find the roots of the given equation, draw a graph.

The graph of the given equation is shown below:

  

From the graph it is seen that the roots of the given equation are $x=1.173$ and $x=2.394$ .

Now, at $x=1.173$ ;

  $\begin{array}{c}y=500x^6\\ =500{\left(1.173\right)}^6\\ =1305\end{array}$

Also, at $x=2.394$ ;

  $\begin{array}{c}y=500x^6\\ =500{\left(2.394\right)}^6\\ =94212\end{array}$

Hence, the required roots of are 1.173, 2.394

Hence, the required roots of are 1.173, 2.394 and the values of $y=500x^6$ are 1305 and 94212.