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How to solve quadratic equations

How to solve quadratic equations

Knowledge of how to solve quadratic equations, it is necessary and students, and students, sometimes it can help an adult in normal life.

There are several specific methods of making.

The solution of quadratic equations

Quadratic equation is an equation of the form a * x ^ 2 + b * x + c = 0. Factor X is the desired variable, a, b, c - the numerical coefficients. Remember that the "+" sign can be changed on the "-" sign.
In order to solve this equation,you need to use the theorem of Vieta, or find a discriminant. The most common way is to find a discriminant, because for some values ​​of a, b, c use the theorem of Vieta's not possible.
To find a discriminant (D), must be writtenformula D = b ^ 2 - 4 * a * c. The value of D may be greater than or equal to zero. If D is greater than or less than zero, then there will be two roots if D = 0, there remains only one root, more precisely one can say that in this case D has two equivalent root. Substitute known coefficients a, b, c in the formula and calculate the value.
Once you've found the discriminant forfinding use formulas x: x (1) = (- b + sqrt {D}) / 2 * a- x (2) = (- b-sqrt {D}) / 2 * a, where sqrt - this function, which means the square root of the number. Considering these expressions, you will find two roots of your equation, then the equation is considered to be a foregone conclusion.
If D is less than zero, it still has roots. In this section of the school is almost not studied. University students should be aware that there is a negative number for the root. From him get rid separating the imaginary part, ie -1 under the root element is always imaginary «i», which is multiplied by the root of the same positive number. For example, if D = sqrt {-20}, is obtained after conversion D = sqrt {20} * i. After this transformation, the solution reduces to the roots of the same finding as described above.
Vieta theorem lies in the selection of the values ​​of x (1)and x (2). Uses two identical equation: x (1) + x (2) = -b- x (1) * x (2) = c. And very important point is the character before the coefficient b, remember that this sign is opposite to that which is in the equation. At first glance it seems that the count x (1) and x (2) is very simple, but at the decision you come up with that number will have to select it.

Elements of the solution of quadratic equations

According to the rules of mathematics, some squarethe equation can be factored: (a + x (1)) * (b-x (2)) = 0, if you through math formulas be converted in this way given a quadratic equation, then go ahead and write the answer. x (1) and x (2) will be equal to a nearby ratios in parentheses, but with the opposite sign.
Also do not forget about the incomplete squareequation. You may be missing some of the components, if this is so, then all its coefficients simply vanish. If before the x ^ 2 and x is worthless, the coefficients a and b are equal to 1.

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