Thursday, 24 July 2008

Quadratic Formula | Common Application Mistakes

Solving Quadratic equation using formula is one of the easiest method and is well-liked by many students.

It is a straight-forward method where we can plug in numbers directly into the quadratic formula to get the answers to the equation.

A general form of the quadratic equation is ax2 + bx + c = 0.

The quadratic formula is x = [-b +- sqrt(b2-4ac) ]/ 2a
where x is the answers to the quadratic equation.

Example: 3x2 + 4x - 1 = 0 is a quadratic equation.

To solve the above, what we need is to identify the value for "a", "b" and c" ( called the coefficient).

Here a = 3, b= 4 and c = -1.
Next putting the numbers of above into the quadratic formula will allow us to get the answers directly. That is it! Nothing difficult!

However mistakes using quadratic formula do occur !

Never see the coefficient properly - that's why!

To apply the quadratic formula, we need to clearly identify the correct coefficient.

Example : 5x + 6x2 - 4 = 0.
Here a = 6 (not 5) since "a" belongs to the x2 term in the quadratic equation.
and b = 5 (not 6) as "b" belongs to the x term of the equation.
c = -4 (no doubt about it)

Message: You do not look for the position of the a, b and c. You look for the term associated with the x2 and x symbol.

  • 'a' always belongs t the term with the power of 2 (e.g. x2),

  • 'b' belongs to the term with power of 1 (e.g. x), and

  • 'c' belongs to the term with power of 0.

Thus to use quadratic formula to solve quadratic equation, the only caution is for you to identify the correct coefficient.

Another common that is always made :

The general quadratic equation is ax2 + bx + c = 0.
NOTE: the equation = 0 .

If the quadratic question is 4x2 - 3x + 2 = x, what then are the value of 'a, 'b' and c'?

We need to ensure that the given equation matches the general quadratic equation form before we can proceed to identify the 'a', 'b' and 'c'.

The answer for above is 'a' = 4, 'b' = -3 -1 = -4, and 'c' = 2.

Advice: Just be careful that the final quadratic equation must = 0 before we do anything.

Maths needs some form of mental discipline to get results. It serves you good in the long run.


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