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Quadratic Equations part C ( Perfect Squared Quadratic Equations)
Posted Date: 19 Mar 2008 Resource Type: Articles/Knowledge Sharing Category: General
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Posted By: mark richards Member Level: Silver
Rating:  Points: 4
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In quadratic equations you must get two values for x, this does not necessarily mean that you must get two different values for x. There is only one exception. It is true that you must get two different values for x but this does not apply to Perfect Squared Quadratic Equations. In Perfect Squared Quadratic Equations (p.s.q.e. for short) you get 2 values but 1 unique solution. What do I mean by this?
Consider the example taken from Quadratic Equations part A (2 posts down)>>>>> 3x^2 -7x -6 =0. This is an ordinary quadratic equation. The solution gives 2 values of x and two unique solutions: x = -2/3 and x = 3.
Now consider the (s.p.q.e) >>>>> x^2 + 4x + 4 =0.
by implementing the split number technique, you will get a result of >>>>>>x^2 + 2x +2x +4 = 0
Factorize> x(x + 2) + 2(x + 2) = 0
Simplify> (x + 2)(x + 2) = 0
Solve>>>> x = -2 x = -2…(2 solutions for x,but 1 unique answer)
The only obstacle in your way is, how can you tell which equations are (p.s.q.e). Consider the form of a quadratic equation:
ax^2 + bx + c = 0
when a = 1 ….as long as (b^2)/4 = c………the quadratic equation is a (p.s.q.e). if a =/= 1 all you have to is divide every term by a!
Consider the equation:
3x^2 - 15x + 18.75 = 0………….a = 3 …then divide by 3
You get: x^2 – 5x + 6.25 = 0……then
use the (b^2)/4 = c, condition. 25/4 = 6.25 ….BINGO!
It is a (p.s.q.e), perform the number split technique and you got your answer. Most people would not recognize it as a (p.s.q.e), which is where practice comes into play. You need to build up your mental to recognize this. If you are now beginning to learn quadratic equations I advise you to do the quadratic formula to solve this one.
Wait! There is an easier way to solve (p.s.q.e). when you have confirm that a quadratic equation is a (p.s.q.e) by ensuring the condition (b^2)/4 works you can solve it in that same line. If you are doing an exam for school you must show the steps to earn marks but in the S.A.T, they don’t watch your steps, they just want the answer, so let us give them the answer. This is to save time in the exam. When you have a (p.s.q.e) the answer for x is always (-b/2). Yes, it is that simple. The only way to master the S.A.T is to master time saving techniques. The Math S.A.T is easy, it is metal stamina is your real test! That concludes Perfect Squared Quadratic Equations
For more details, visit http://mathssat.blogspot.com/
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