How do you solve a quadratic equation without using a formula?
3 Answers
Explanation:
See below.
Explanation:
There are different ways, but it will be dependent on the particular quadratic.
Works for all quadratics
Works for all quadratics
- Factoring
Can be difficult sometimes to find factors without knowing roots
- Graphically
Results from graphs are generally not very accurate.
- Iteration
This requires knowing roughly where the roots lie, in order to get convergence. A common iterative process is the Newton Raphson method.
So there other methods, but they are not as convenient as a formula.
How about geometrically...
Explanation:
No formula?
How about...
This solves the quadratic equation:
#x^2-a = 0#
To construct the square root of a positive real number geometrically, construct a semicircular arc with diameter
With a bit more work, you can find real solutions of any quadratic geometrically.