Chapter P.5, Problem 31E

Solution

To solve the equation graphically by finding x-intercepts, $x^3+x^2+2x-3=0$ .

  $x=\{0\cdot 844\}$

Given:

The equation is, $x^3+x^2+2x-3=0$

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:

  $x^3+x^2+2x-3=0$

Let y=0

So $x^3+x^2+2x-3=y$

The graph of $x^3+x^2+2x-3=y$

is shown below:

  

Since the graph intersects the x- axis at $x=0\cdot 844$ so the solutions are $x=\{0\cdot 844\}$

Thus, the solution of the given equation is $x=\{0\cdot 844\}$ .