Quadratic equation
If the highest power of a variable is 2, then we talk about quadratic equations. The solution is found by substituting multipliers into the formula.
First, the equation must be rewritten in the standard form
Solutions are
If the discriminant (expression inside the square root)
- > 0, there are two different real solutions.
- = 0, there is only one real solution.
- < 0, there is no real solution but the complex solution can be found.
Example 1. Solve
The equation is in a standard form, so and By substituting these to the formula, we get the solutions:
Example 2. Solve equation
The equation is in a standard form, so and , because constant is missing from the original equation. By substituting these to the formula, we get the solutions:
Example 3. Solve equation
The equation is in a standard form, so (linear term is missing) and By substituting these to the formula, we get the solutions:
Example 4. Solve
Let us simplify the equation first by removing brackets and combining like terms:
As the equations is of degree two (the highest power of the variable), it must be given in the standard form. Values of parameters in a formula are always looked from a standard form.