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How to Solve Quadratic Equations


Many students find it difficult to solve the quadratic equations especially when they only begin to practice. But you will see that quadratic equations are not the most sophisticated thing in the world after you will successfully sole some of them. Practice is quite important in this case. If you have a good memory you may member some basic frequent quadratic equations and the right answers will pop up in your mind at once. The quadratic equations are the basis of the future calculations that you will face while studying math.

To solve quadratic equations is not that difficult as it may seem to be at the first time. The main things is to memorize the algorithm and to choose the best way to solve your equation. To begin with the quadratic equations are the equations of the following type: axx + bx + c = 0. X is called the switching variable and a, b and c are some integers. Take into consideration that a and b are not equal null.



Discriminant Formula

The first way to solve the quadratic equations is to use the discriminant formula. There are two forms of discriminant (D). The first one is D = bb-4ac. You may easily see that according to that formula that x equals -b plus or minus the square root of the discriminant and then divided by a multiplied y 2.

If b is the even integer you may use another variant of the discriminant formula. That is D/4 = (b/2)(b/2)-ac. In that way you will also come to the final formula according to which you may find the x described above.


Vieta Theorem

The second way to solve the quadratic equations is to use the Vieta theorem. You don't need to count any complicated discriminant formula to use that method. But you should be able to calculate and guesstimate the integers well enough. The Vieta theorem allows to assume the fact that the sum of the two x's is equal -b/a and one x multiplied by the other one makes the integer equal to c/a. If a = 1 the sum of the roots will be equal -b and their product integer will be equal c. This is sensible to use the Vieta theorem to check the answers during the test for instance.



The third way to solve the quadratic equations is to build a chart. That may be either a line of a reciprocal spiral. Let us take a simple quadratic equation xx + x + 1 = 0 as the example. You may see that you should build two charts: y = x2 and y = x + 1.

The first minor equation is typical of the quadratic function. Its chart looks like a parabolic curve. The second minor equation is typical of the affine function. Its chart is a line. Draw the two charts in one and the same frame of reference. The two chart will cross each other in two points which coordinates will show you the answers.


  • Don't try to guess the answers even if the quadratic equation seem too primitive to you.
  • Don't give up solving the quadratic equation even if you can't cope with it at once. Switch to solving the task of some other type than return to the equation. You will see the way to solve it easily.
  • Don't peep in the answers before you sole the quadratic equation on your own. That will prevent your mind from thinking properly.
  • Avoid using the Vieta theorem for the complicated quadratic equations if you can't calculate and guess the integers well. That will mislead you.



You should develop the serious approach to studying maths. The matter is that cheating or using the calculators will have only the temporal effect. It is important to understand how to solve the equations but not to look up the right answer in the end of the exercise book. Even if you are experiencing some difficulties now go ahead and do your best to grasp the certain method of counting fully. Good luck in your studies!

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