(x+5)(x-2) 0 Graph On Number Line

Jasonbradley

4 min read

·

Jun 17, 2024

33

Share

Graphing the Solution to (x+5)(x-2) = 0 on a Number Line

To graph the solution to the equation (x+5)(x-2) = 0 on a number line, we need to find the values of x that make the equation true.

Finding the Roots

The equation (x+5)(x-2) = 0 is in factored form. This makes it easy to find the roots, also known as the solutions or zeros, of the equation. The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Therefore, for the equation (x+5)(x-2) = 0 to be true, either:

• x + 5 = 0 or
• x - 2 = 0

Solving for x in each equation, we get:

• x = -5
• x = 2

Graphing on the Number Line

1. Draw a number line: Draw a horizontal line and mark points representing -5 and 2 on it.

2. Mark the roots: Place a solid dot above each of the points representing the roots (-5 and 2) on the number line.

3. Divide the number line: The roots (-5 and 2) divide the number line into three intervals:

   • x < -5
   • -5 < x < 2
   • x > 2

4. Test the intervals: Pick a test value within each interval and substitute it into the original equation (x+5)(x-2) = 0. Determine if the result is positive or negative.

   • x < -5: Let's choose x = -6. (-6+5)(-6-2) = (-1)(-8) = 8 > 0. Therefore, the solution in this interval is positive.

   • -5 < x < 2: Let's choose x = 0. (0+5)(0-2) = (5)(-2) = -10 < 0. Therefore, the solution in this interval is negative.

   • x > 2: Let's choose x = 3. (3+5)(3-2) = (8)(1) = 8 > 0. Therefore, the solution in this interval is positive.

5. Shade the solution: Since the equation is (x+5)(x-2) = 0, we are looking for the values of x that make the expression equal to zero. This occurs only at the roots, x = -5 and x = 2.

   • We mark these points with a solid dot to indicate that they are included in the solution.

   • The solution is represented by the two points on the number line.

Conclusion

The graph of the solution to the equation (x+5)(x-2) = 0 on a number line consists of two solid dots at x = -5 and x = 2. This visually represents that the only values of x that satisfy the equation are -5 and 2.