Quadratic Formula

[nycmathguy]

We must use the quadratic formula when an equation cannot be factored. Yes?

 

[MathLover1]

yes

 

[nycmathguy]

yes

To use a quadratic equation, the equation must be in the form ax^2 + bx + c = 0, where a = b = c = constants.

 

[Country Boy]

We must use the quadratic formula when an equation cannot be factored. Yes?

NO! We can "complete the square"!

For example, x^2- 8x+ 3= 0 cannot be factored. But it can be written as x^2- 8x= -3. "Complete the square" by adding 16 to both sides: x^2- 8x+ 16= -3+ 16.
(x- 4)^2= 13.
x- 4= +/- sqrt(13).

The solutions are x= 4+ sqrt(13) and x= 4- sqrt(13).

Of course, those are the solutions the quadratic formula would give us.

 

[Country Boy]

To use a quadratic equation, the equation must be in the form ax^2 + bx + c = 0, where a = b = c = constants.

You mean "to use the quadratic formula".

And any quadratic equation can be easily put in that form.

 

[nycmathguy]

NO! We can "complete the square"!

For example, x^2- 8x+ 3= 0 cannot be factored. But it can be written as x^2- 8x= -3. "Complete the square" by adding 16 to both sides: x^2- 8x+ 16= -3+ 16.
(x- 4)^2= 13.
x- 4= +/- sqrt(13).

The solutions are x= 4+ sqrt(13) and x= 4- sqrt(13).

Of course, those are the solutions the quadratic formula would give us.

You said no but MathLover1 said yes. Now, I am confused.

 

[nycmathguy]

You mean "to use the quadratic formula".

And any quadratic equation can be easily put in that form.

Yes, of course to use in the quadratic formula.