Solving Quadratic Equations Using the Quadratic Formula

 When you solve an equation of the form ax² + bx + c = 0, consider the following:

• If a = 0, then the equation can be written bx + c = 0.

This is a linear equation, not a quadratic equation.

So we cannot use the quadratic formula to solve it.

• If b = 0, then the equation can be written ax² + c = 0.

We can solve using the quadratic formula with b = 0.

However, it takes fewer steps to solve this equation using the Square Root Property.

• If c = 0, then the equation can be written ax² + bx = 0.

We can solve using the quadratic formula with c = 0.

However, it takes fewer steps to solve this equation by factoring.

Note:

Here’s an example when a = 0:

3x + 5 = 0

a = 0, b = 3, c = 5

This is a linear equation.

Here’s an example when b = 0:

2x² + 5 = 0

a = 2, b = 0, c = 5

Here’s an example when c = 0:

2x² + 3x = 0

a = 2, b = 3, c = 5