The simplest way to solve “ax2 + bx +c = 0“ or any other quadratic equation is by factorizing the equation and set each factor equal to zero and then simplify. However, most of the times the quadratic equations are messy and doesn’t factor at all.
When factoring is not a solution then the best way to solve any quadratic equation is using Quadratic Formula which will always be helpful to find the solution for any quadratic equation.
The Quadratic Formula:
For any ax2 + bx +c = 0 equation, the quadratic formula is given by:
Where “a”, “b”, and “c” are numbers from ax2 + bx +c = 0 and a≠0 and b²-4ac ≥ 0.
- “2a” in the denominator of the formula is underneath everything above and not just under the square root.
- Don’t forget that it is “2a” in the denominator and not just a plain “2”.
- Don’t forget to add “plus/minus” signs in the formula or you will mess everything up.
- “b²” means the square of all the values of b including its sign.
Within the Quadratic formula, the expression b²-4ac ≥ 0 is called the discriminant and it can be used to find out how many possible solutions are there for the given quadratic equation.
If b²-4ac > 0| 2 Solutions
If b²-4ac = 0 | 1 Solution
If b²-4ac < 0 | No Real Solution