Chapter P.5, Problem 29E

Solution

To solve the equation graphically by finding x-intercepts. Confirm by using factoring the equation, $x^2+x-1=0$ .

  $x=\{-1\cdot 618,0\cdot 618\}$

Given:

The equation is, $x^2+x-1=0$

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:

  $x^2+x-1=0$

Let y=0

So $x^2+x-1=y$

The graph of $x^2+x-1=y$

is shown below:

  

Since the graph intersects the x- axis at $x=-1\cdot 618$ and $x=0\cdot 618$ , so the solutions are $x=\{-1\cdot 618,0\cdot 618\}$

Thus, the solution of the given equation is $x=\{-1\cdot 618,0\cdot 618\}$ .