Solving the Quadratic Equation x² – 11x + 28 = 0
Quadratic equations are fundamental in algebra. In this guide, we will solve the equation x² – 11x + 28 = 0 using the quadratic formula.
Understanding the Quadratic Formula
The quadratic formula is given by:
Where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
For the equation x² – 11x + 28 = 0:
- a = 1
- b = -11
- c = 28
Alternative Solution: Factoring Method
Since the given quadratic equation is simple, we can also solve it by factoring.
- Find two numbers that multiply by 28 and add up to 11.
- The numbers are 7 and 4.
- Rewrite the middle term:
- Factor out common terms:
- Take the common factor:
- Solve for x:
- x – 7 = 0 → x = 7
- x – 4 = 0 → x = 4
This confirms our previous solution.
Visual Representation
To better understand, here is a graphical representation of the function y = x² – 11x + 28. The graph intersects the x-axis at x = 7 and x = 4, verifying the roots.
(Insert an appropriate quadratic equation graph image here)
Summary
- The roots of x² – 11x + 28 = 0 are x = 7 and x = 4.
- We solved the equation using both the quadratic formula and factoring method.
- The graph confirms the accuracy of our solution.
- By following this guide, you can solve similar quadratic equations efficiently.
Related Topics
External References
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