Chapter P.5, Problem 5E

Solution

To solve the equation graphically by finding x-intercepts. Confirm by using factoring the equation, $x(3x-7)=6$ .

  $x=\{-0\cdot 667,3\}$

Given:

The equation is, $x(3x-7)=6$

Concept Used:

• The x-intercept is given by y = 0: 0 = ax² + bx + c. Isolating the square and then applying the square root property.
• The discriminant gives the number of x-intercepts of a quadratic function, because it gives us the number of solutions to ax² + bx + c = 0.

Calculation:

  $\begin{array}{l}x(3x-7)=6\\ 3x^2-7x=6\\ 3x^2-7x-6=0\end{array}$

Let y=0

So $3x^2-7x-6=y$

The graph of $3x^2-7x-6=y$

is shown below:

  

Since the graph intersects the x- axis at $x=-0\cdot 667$ and $x=3$ , so the solutions are $x=\{-0\cdot 667,3\}$

Now solve by factoring method-

  $\begin{array}{c}3x^2-7x-6=0\\ 3x^2-(9-2)x-6=0\\ 3x^2-9x+2x-6=0\\ 3x(x-3)+2(x-3)=0\\ (3x+2)(x-3)=0\\ (3x+2)=0\\ 3x=-2\\ x=-\frac{2}{3}\\ x=-0\cdot 667\\ (x-3)=0\\ x=3\\ x=\{-0\cdot 667,3\}\end{array}$

Both from graphically and factoring solution is same i.e $x=\{-0\cdot 667,3\}$

Thus, the solution of the given equation is $x=\{-0\cdot 667,3\}$ .