Alfi Blog

Alfi Blog

Alfi Blog


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The Quadratic Formula - 1

The quadratic formula can be messy to compute when any of a, b, or c are fractions or decimals. You can get around this by multiplying both sides of the equation by the least common denominator or some power of ten.

The Quadratic Formula

The Quadratic Formula

 

The other main approach to solving quadratic equations comes from the fact that x2 = k implies x = k, –k and a technique called completing the square. The solutions to ax2 + bx + c = 0 are:

Quadratic Equations - 2

Sometimes using the fact that x2 = k implies x = ±k can be used to solve quadratic equations. For instance, if x2 = 9, then x = 3 or –3 because 32 = 9 and (–3)2 = 9. This method works if the equation can be put in the form ax2 – c = 0, where a and c are not negative.

Quadratic Equations - 1

Not all quadratic expressions will be as easy to factor as the previous examples and problems were. Sometimes you will need to multiply or divide both sides of the equation by a number. Because zero multiplied or divided by any nonzero number is still zero, only one side of the equation will change. Keep in mind that not all quadratic expressions can be factored using rational numbers (fractions) or even real numbers. Fortunately there

Quadratic Equations

Quadratic Equations

 

A quadratic equation is one that can be put in the form ax2 + bx + c = 0 where a, b, and c are numbers and a is not zero (b and/or c might be zero).

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